Search

Steady surface waves in a two-dimensional channel are considered. We study bifurcations, which occur on a branch of Stokes water waves starting from a uniform stream solution. Two types of bifurcations are considered: bifurcations in the class of Stokes waves (Stokes bifurcation) and bifurcations in a class of periodic waves with the period M times the period of the Stokes wave (M-subharmonic bifurcation). If we consider the first Stokes bifurcation point then there are no M-subharmonic bifurcations before this point and there exists M-subharmonic bifurcation points after the first Stokes bifurcation for sufficiently large M, which approach the Stokes bifurcation point when M→∞. Moreover the set of M-subharmonic bifurcating solutions is a closed connected continuum. We give also a more detailed description of this connected set in terms of the set of its limit points, which must contain extreme waves, or overhanging waves, or solitary waves or waves with stagnation on the bottom, or Stokes bifurcation points different from the initial one., Funding Agencies|Swedish Research Council (VR) [2017-03837]

Steady surface waves in a two-dimensional channel are considered. We study bifurcations, which occur on a branch of Stokes water waves starting from a uniform stream solution. Two types of bifurcations are considered: bifurcations in the class of Stokes waves (Stokes bifurcation) and bifurcations in a class of periodic waves with the period M times the period of the Stokes wave (M-subharmonic bifurcation). If we consider the first Stokes bifurcation point then there are no M-subharmonic bifurcations before this point and there exists M-subharmonic bifurcation points after the first Stokes bifurcation for sufficiently large M, which approach the Stokes bifurcation point when M→∞. Moreover the set of M-subharmonic bifurcating solutions is a closed connected continuum. We give also a more detailed description of this connected set in terms of the set of its limit points, which must contain extreme waves, or overhanging waves, or solitary waves or waves with stagnation on the bottom, or Stokes bifurcation points different from the initial one., Funding Agencies|Swedish Research Council (VR) [2017-03837]

Steady surface waves in a two-dimensional channel are considered. We study bifurcations, which occur on a branch of Stokes water waves starting from a uniform stream solution. Two types of bifurcations are considered: bifurcations in the class of Stokes waves (Stokes bifurcation) and bifurcations in a class of periodic waves with the period M times the period of the Stokes wave (M-subharmonic bifurcation). If we consider the first Stokes bifurcation point then there are no M-subharmonic bifurcations before this point and there exists M-subharmonic bifurcation points after the first Stokes bifurcation for sufficiently large M, which approach the Stokes bifurcation point when M→∞. Moreover the set of M-subharmonic bifurcating solutions is a closed connected continuum. We give also a more detailed description of this connected set in terms of the set of its limit points, which must contain extreme waves, or overhanging waves, or solitary waves or waves with stagnation on the bottom, or Stokes bifurcation points different from the initial one., Funding Agencies|Swedish Research Council (VR) [2017-03837]

Steady surface waves in a two-dimensional channel are considered. We study bifurcations, which occur on a branch of Stokes water waves starting from a uniform stream solution. Two types of bifurcations are considered: bifurcations in the class of Stokes waves (Stokes bifurcation) and bifurcations in a class of periodic waves with the period M times the period of the Stokes wave (M-subharmonic bifurcation). If we consider the first Stokes bifurcation point then there are no M-subharmonic bifurcations before this point and there exists M-subharmonic bifurcation points after the first Stokes bifurcation for sufficiently large M, which approach the Stokes bifurcation point when M→∞. Moreover the set of M-subharmonic bifurcating solutions is a closed connected continuum. We give also a more detailed description of this connected set in terms of the set of its limit points, which must contain extreme waves, or overhanging waves, or solitary waves or waves with stagnation on the bottom, or Stokes bifurcation points different from the initial one., Funding Agencies|Swedish Research Council (VR) [2017-03837]

Steady surface waves in a two-dimensional channel are considered. We study bifurcations, which occur on a branch of Stokes water waves starting from a uniform stream solution. Two types of bifurcations are considered: bifurcations in the class of Stokes waves (Stokes bifurcation) and bifurcations in a class of periodic waves with the period M times the period of the Stokes wave (M-subharmonic bifurcation). If we consider the first Stokes bifurcation point then there are no M-subharmonic bifurcations before this point and there exists M-subharmonic bifurcation points after the first Stokes bifurcation for sufficiently large M, which approach the Stokes bifurcation point when M→∞. Moreover the set of M-subharmonic bifurcating solutions is a closed connected continuum. We give also a more detailed description of this connected set in terms of the set of its limit points, which must contain extreme waves, or overhanging waves, or solitary waves or waves with stagnation on the bottom, or Stokes bifurcation points different from the initial one., Funding Agencies|Swedish Research Council (VR) [2017-03837]

We consider the two-dimensional problem for steady water waves with vorticity on water of finite depth. While neglecting the effects of surface tension we construct connected families of large amplitude periodic waves approaching a limiting wave, which is either a solitary wave, the highest solitary wave, the highest Stokes wave or a Stokes wave with a breaking profile. In particular, when the vorticity is nonnegative we prove the existence of highest Stokes waves with an included angle of 120 degrees. In contrast to previous studies, we fix the Bernoulli constant and consider the wavelength as a bifurcation parameter, which guarantees that the limiting wave has a finite depth. In fact, this is the first rigorous proof of the existence of extreme Stokes waves with vorticity on water of finite depth. Aside from the existence of highest waves, we provide a new result about the regularity of Stokes waves of arbitrary amplitude (including extreme waves). Furthermore, we prove several new facts about steady waves, such as a lower bound for the wavelength of Stokes waves, while also eliminating a possibility of the wave breaking for waves with non-negative vorticity., Funding Agencies|Swedish Research Council (VR) [2017-03837]

We consider a steady state heat conduction problem in a thin plate. In the application, it is used to connect two cylindrical containers and fix their relative positions. At the same time it serves to measure the temperature on the inner cylinder. We derive a two dimensional mathematical model, and use it to approximate the heat conduction in the thin plate. Since the plate has sharp edges on the sides the resulting problem is described by a degenerate elliptic equation. To find the temperature in the interior part from the exterior measurements, we formulate the problem as a Cauchy problem for stationary heat equation. We also reformulate the Cauchy problem as an operator equation, with a compact operator, and apply the Landweber iteration method to solve the equation. The case of the degenerate elliptic equation has not been previously studied in this context. For numerical computation, we consider the case where noisy data is present and analyse the convergence., Funding Agencies|Linkping University

We consider the two-dimensional problem for steady water waves with vorticity on water of finite depth. While neglecting the effects of surface tension we construct connected families of large amplitude periodic waves approaching a limiting wave, which is either a solitary wave, the highest solitary wave, the highest Stokes wave or a Stokes wave with a breaking profile. In particular, when the vorticity is nonnegative we prove the existence of highest Stokes waves with an included angle of 120 degrees. In contrast to previous studies, we fix the Bernoulli constant and consider the wavelength as a bifurcation parameter, which guarantees that the limiting wave has a finite depth. In fact, this is the first rigorous proof of the existence of extreme Stokes waves with vorticity on water of finite depth. Aside from the existence of highest waves, we provide a new result about the regularity of Stokes waves of arbitrary amplitude (including extreme waves). Furthermore, we prove several new facts about steady waves, such as a lower bound for the wavelength of Stokes waves, while also eliminating a possibility of the wave breaking for waves with non-negative vorticity., Funding Agencies|Swedish Research Council (VR) [2017-03837]

We consider a steady state heat conduction problem in a thin plate. In the application, it is used to connect two cylindrical containers and fix their relative positions. At the same time it serves to measure the temperature on the inner cylinder. We derive a two dimensional mathematical model, and use it to approximate the heat conduction in the thin plate. Since the plate has sharp edges on the sides the resulting problem is described by a degenerate elliptic equation. To find the temperature in the interior part from the exterior measurements, we formulate the problem as a Cauchy problem for stationary heat equation. We also reformulate the Cauchy problem as an operator equation, with a compact operator, and apply the Landweber iteration method to solve the equation. The case of the degenerate elliptic equation has not been previously studied in this context. For numerical computation, we consider the case where noisy data is present and analyse the convergence., Funding Agencies|Linkping University

We consider the two-dimensional problem for steady water waves with vorticity on water of finite depth. While neglecting the effects of surface tension we construct connected families of large amplitude periodic waves approaching a limiting wave, which is either a solitary wave, the highest solitary wave, the highest Stokes wave or a Stokes wave with a breaking profile. In particular, when the vorticity is nonnegative we prove the existence of highest Stokes waves with an included angle of 120 degrees. In contrast to previous studies, we fix the Bernoulli constant and consider the wavelength as a bifurcation parameter, which guarantees that the limiting wave has a finite depth. In fact, this is the first rigorous proof of the existence of extreme Stokes waves with vorticity on water of finite depth. Aside from the existence of highest waves, we provide a new result about the regularity of Stokes waves of arbitrary amplitude (including extreme waves). Furthermore, we prove several new facts about steady waves, such as a lower bound for the wavelength of Stokes waves, while also eliminating a possibility of the wave breaking for waves with non-negative vorticity., Funding Agencies|Swedish Research Council (VR) [2017-03837]

We consider a steady state heat conduction problem in a thin plate. In the application, it is used to connect two cylindrical containers and fix their relative positions. At the same time it serves to measure the temperature on the inner cylinder. We derive a two dimensional mathematical model, and use it to approximate the heat conduction in the thin plate. Since the plate has sharp edges on the sides the resulting problem is described by a degenerate elliptic equation. To find the temperature in the interior part from the exterior measurements, we formulate the problem as a Cauchy problem for stationary heat equation. We also reformulate the Cauchy problem as an operator equation, with a compact operator, and apply the Landweber iteration method to solve the equation. The case of the degenerate elliptic equation has not been previously studied in this context. For numerical computation, we consider the case where noisy data is present and analyse the convergence., Funding Agencies|Linkping University

Der Beitrag liefert eine kurze Beschreibung der demographischen Lage in Russland und berücksichtigt dabei auch die Folgen der Corona-Krise, des aktuellen Krieges und der Sanktionen. Auch durch die Altersstruktur der russischen Bevölkerung entstehende Schwierigkeiten werden angesprochen, die in erheblichem Maße den Bevölkerungsschwund und Alterungsprozesse beeinflusst. Darüber hinaus werden dadurch wirtschaftliche Planungsprozesse erschwert. Insgesamt steht Russland als ein im Grunde entwickeltes Land da und weist für derlei Länder durchschnittliche Niveaus der Alterung und der Geburtenraten auf. Allerdings ist die Sterblichkeit höher. Russland ist relativ attraktiv für Migrant:innen, doch sind die Folgen für Geburtenraten und Migrationsbewegungen nach dem Februar 2022 nur schwer abzuschätzen.

Untill 1980 one of the main subjects of study in the theory of nonlinear water waves were the Stokes and solitary waves (regular waves). To that time small amplitude regular waves were constructed and the existence of large amplitude water waves of the same type was proved by using branches of water waves starting from a trivial (horizontal) wave and ending at extreme waves. Then in papers Chen & Saffman [7] and Saffman [32] numerical evidence was presented for existence of other type of waves as a result of bifurcations from a branch of ir-rotational Stokes waves on flow of infinite depth. It was demonstrated that the Stokes branch has infinitely many bifurcation points when it approaches the extreme wave and periodic waves with several crests of different height on the period bifurcate from the main branch. The only theoretical works dealing with this phenomenon are Buffoni, Dancer & Toland [4,5] where it was proved the existence of sub-harmonic bifurcations bifurcating from the Stokes branch for the ir-rotational flow of infinite depth approaching the extreme wave.The aim of this paper is to develop new tools and give rigorous proof of existence of subharmonic bifurcations in the case of rotational flows of finite depth. The whole paper is devoted to the proof of this result formulated in Theorem 5.4., Funding Agencies|Swedish Research Council (VR) [2017-03837]

We give a quite simple approach how to prove the absence of loops in bifurcation branches of water waves in rotational case with arbitrary vorticity distribution. The supporting flow may contain stagnation points and critical layers and water surface is allowed to be overhanging. Monotonicity properties of the free surface are presented. Especially simple criterium of absence of loops is given for bifurcation branches when the bifurcation parameter is the water wave period. We show that there are no loops if you start from a water wave with a positive/negative vertical component of velocity on the positive half period., Funding Agencies|Swedish Research Council (VR); [2017-03837]

We give a quite simple approach how to prove the absence of loops in bifurcation branches of water waves in rotational case with arbitrary vorticity distribution. The supporting flow may contain stagnation points and critical layers and water surface is allowed to be overhanging. Monotonicity properties of the free surface are presented. Especially simple criterium of absence of loops is given for bifurcation branches when the bifurcation parameter is the water wave period. We show that there are no loops if you start from a water wave with a positive/negative vertical component of velocity on the positive half period., Funding Agencies|Swedish Research Council (VR); [2017-03837]

The authors consider the Neumann problem for the nonstationary Stokes system in a two-dimensional angle or a three-dimensional cone. They obtain existence and uniqueness results for solutions in weighted Sobolev spaces and prove a regularity assertion for the solutions.

We give a quite simple approach how to prove the absence of loops in bifurcation branches of water waves in rotational case with arbitrary vorticity distribution. The supporting flow may contain stagnation points and critical layers and water surface is allowed to be overhanging. Monotonicity properties of the free surface are presented. Especially simple criterium of absence of loops is given for bifurcation branches when the bifurcation parameter is the water wave period. We show that there are no loops if you start from a water wave with a positive/negative vertical component of velocity on the positive half period., Funding Agencies|Swedish Research Council (VR); [2017-03837]

Untill 1980 one of the main subjects of study in the theory of nonlinear water waves were the Stokes and solitary waves (regular waves). To that time small amplitude regular waves were constructed and the existence of large amplitude water waves of the same type was proved by using branches of water waves starting from a trivial (horizontal) wave and ending at extreme waves. Then in papers Chen & Saffman [7] and Saffman [32] numerical evidence was presented for existence of other type of waves as a result of bifurcations from a branch of ir-rotational Stokes waves on flow of infinite depth. It was demonstrated that the Stokes branch has infinitely many bifurcation points when it approaches the extreme wave and periodic waves with several crests of different height on the period bifurcate from the main branch. The only theoretical works dealing with this phenomenon are Buffoni, Dancer & Toland [4,5] where it was proved the existence of sub-harmonic bifurcations bifurcating from the Stokes branch for the ir-rotational flow of infinite depth approaching the extreme wave.The aim of this paper is to develop new tools and give rigorous proof of existence of subharmonic bifurcations in the case of rotational flows of finite depth. The whole paper is devoted to the proof of this result formulated in Theorem 5.4., Funding Agencies|Swedish Research Council (VR) [2017-03837]

The authors consider the Neumann problem for the nonstationary Stokes system in a two-dimensional angle or a three-dimensional cone. They obtain existence and uniqueness results for solutions in weighted Sobolev spaces and prove a regularity assertion for the solutions.

Untill 1980 one of the main subjects of study in the theory of nonlinear water waves were the Stokes and solitary waves (regular waves). To that time small amplitude regular waves were constructed and the existence of large amplitude water waves of the same type was proved by using branches of water waves starting from a trivial (horizontal) wave and ending at extreme waves. Then in papers Chen & Saffman [7] and Saffman [32] numerical evidence was presented for existence of other type of waves as a result of bifurcations from a branch of ir-rotational Stokes waves on flow of infinite depth. It was demonstrated that the Stokes branch has infinitely many bifurcation points when it approaches the extreme wave and periodic waves with several crests of different height on the period bifurcate from the main branch. The only theoretical works dealing with this phenomenon are Buffoni, Dancer & Toland [4,5] where it was proved the existence of sub-harmonic bifurcations bifurcating from the Stokes branch for the ir-rotational flow of infinite depth approaching the extreme wave.The aim of this paper is to develop new tools and give rigorous proof of existence of subharmonic bifurcations in the case of rotational flows of finite depth. The whole paper is devoted to the proof of this result formulated in Theorem 5.4., Funding Agencies|Swedish Research Council (VR) [2017-03837]

The authors consider the Neumann problem for the nonstationary Stokes system in a two-dimensional angle or a three-dimensional cone. They obtain existence and uniqueness results for solutions in weighted Sobolev spaces and prove a regularity assertion for the solutions.

We consider an inverse problem for the Helmholtz equation of reconstructing a solution from measurements taken on a segment inside a semi-infinite strip. Homogeneous Neumann conditions are prescribed on both side boundaries of the strip and an unknown Dirichlet condition on the remaining part of the boundary. Additional complexity is that the radiation condition at infinity is unknown. Our aim is to find the unknown function in the Dirichlet boundary condition and the radiation condition. Such problems appear in acoustics to determine acoustical sources and surface vibrations from acoustic field measurements. The problem is split into two sub-problems, a well-posed and an ill-posed problem. We analyse the theoretical properties of both problems; in particular, we show that the radiation condition is described by a stable non-linear problem. The second problem is ill-posed, and we use the Landweber iteration method together with the discrepancy principle to regularize it. Numerical tests show that the approach works well.

We consider the two-dimensional problem for steady water waves with vorticity on water of finite depth. While neglecting the effects of surface tension we construct connected families of large amplitude periodic waves approaching a limiting wave, which is either a solitary wave, the highest solitary wave, the highest Stokes wave or a Stokes wave with a breaking profile. In particular, when the vorticity is nonnegative we prove the existence of highest Stokes waves with an included angle of 120 degrees. In contrast to previous studies, we fix the Bernoulli constant and consider the wavelength as a bifurcation parameter, which guarantees that the limiting wave has a finite depth. In fact, this is the first rigorous proof of the existence of extreme Stokes waves with vorticity on water of finite depth. Aside from the existence of highest waves, we provide a new result about the regularity of Stokes waves of arbitrary amplitude (including extreme waves). Furthermore, we prove several new facts about steady waves, such as a lower bound for the wavelength of Stokes waves, while also eliminating a possibility of the wave breaking for waves with non-negative vorticity., Funding Agencies|Swedish Research Council (VR) [2017-03837]

Untill 1980 one of the main subjects of study in the theory of nonlinear water waves were the Stokes and solitary waves (regular waves). To that time small amplitude regular waves were constructed and the existence of large amplitude water waves of the same type was proved by using branches of water waves starting from a trivial (horizontal) wave and ending at extreme waves. Then in papers Chen & Saffman [7] and Saffman [32] numerical evidence was presented for existence of other type of waves as a result of bifurcations from a branch of ir-rotational Stokes waves on flow of infinite depth. It was demonstrated that the Stokes branch has infinitely many bifurcation points when it approaches the extreme wave and periodic waves with several crests of different height on the period bifurcate from the main branch. The only theoretical works dealing with this phenomenon are Buffoni, Dancer & Toland [4,5] where it was proved the existence of sub-harmonic bifurcations bifurcating from the Stokes branch for the ir-rotational flow of infinite depth approaching the extreme wave.The aim of this paper is to develop new tools and give rigorous proof of existence of subharmonic bifurcations in the case of rotational flows of finite depth. The whole paper is devoted to the proof of this result formulated in Theorem 5.4., Funding Agencies|Swedish Research Council (VR) [2017-03837]

We consider the Cauchy problem for the Helmholtz equation with a domain in with N cylindrical outlets to infinity with bounded inclusions in . Cauchy data are prescribed on the boundary of the bounded domains and the aim is to find solution on the unbounded part of the boundary. In 1989, Kozlov and Mazya proposed an alternating iterative method for solving Cauchy problems associated with elliptic, selfadjoint and positive-definite operators in bounded domains. Different variants of this method for solving Cauchy problems associated with Helmholtz-type operators exists. We consider the variant proposed by Berntsson, Kozlov, Mpinganzima and Turesson (2018) for bounded domains and derive the necessary conditions for the convergence of the procedure in unbounded domains. For the numerical implementation, a finite difference method is used to solve the problem in a simple rectangular domain in R-2 that represent a truncated infinite strip. The numerical results shows that by appropriate truncation of the domain and with appropriate choice of the Robin parameters mu(0) and mu(1), the Robin-Dirichlet alternating iterative procedure is convergent.

The authors consider the Neumann problem for the nonstationary Stokes system in a two-dimensional angle or a three-dimensional cone. They obtain existence and uniqueness results for solutions in weighted Sobolev spaces and prove a regularity assertion for the solutions.

We consider a spectral problem associated with steady water waves of extreme form on the free surface of a rotational flow. It is proved that the spectrum of this problem contains arbitrary large negative eigenvalues and they are simple. Moreover, the asymptotics of such eigenvalues is obtained., Funding Agencies|Swedish Research Council (VR); [2017-03837]

We give a quite simple approach how to prove the absence of loops in bifurcation branches of water waves in rotational case with arbitrary vorticity distribution. The supporting flow may contain stagnation points and critical layers and water surface is allowed to be overhanging. Monotonicity properties of the free surface are presented. Especially simple criterium of absence of loops is given for bifurcation branches when the bifurcation parameter is the water wave period. We show that there are no loops if you start from a water wave with a positive/negative vertical component of velocity on the positive half period., Funding Agencies|Swedish Research Council (VR); [2017-03837]

Untill 1980 one of the main subjects of study in the theory of nonlinear water waves were the Stokes and solitary waves (regular waves). To that time small amplitude regular waves were constructed and the existence of large amplitude water waves of the same type was proved by using branches of water waves starting from a trivial (horizontal) wave and ending at extreme waves. Then in papers Chen & Saffman [7] and Saffman [32] numerical evidence was presented for existence of other type of waves as a result of bifurcations from a branch of ir-rotational Stokes waves on flow of infinite depth. It was demonstrated that the Stokes branch has infinitely many bifurcation points when it approaches the extreme wave and periodic waves with several crests of different height on the period bifurcate from the main branch. The only theoretical works dealing with this phenomenon are Buffoni, Dancer & Toland [4,5] where it was proved the existence of sub-harmonic bifurcations bifurcating from the Stokes branch for the ir-rotational flow of infinite depth approaching the extreme wave.The aim of this paper is to develop new tools and give rigorous proof of existence of subharmonic bifurcations in the case of rotational flows of finite depth. The whole paper is devoted to the proof of this result formulated in Theorem 5.4., Funding Agencies|Swedish Research Council (VR) [2017-03837]

The authors consider the Neumann problem for the nonstationary Stokes system in a two-dimensional angle or a three-dimensional cone. They obtain existence and uniqueness results for solutions in weighted Sobolev spaces and prove a regularity assertion for the solutions.

We give a quite simple approach how to prove the absence of loops in bifurcation branches of water waves in rotational case with arbitrary vorticity distribution. The supporting flow may contain stagnation points and critical layers and water surface is allowed to be overhanging. Monotonicity properties of the free surface are presented. Especially simple criterium of absence of loops is given for bifurcation branches when the bifurcation parameter is the water wave period. We show that there are no loops if you start from a water wave with a positive/negative vertical component of velocity on the positive half period., Funding Agencies|Swedish Research Council (VR); [2017-03837]

We consider the two-dimensional problem for steady water waves with vorticity on water of finite depth. While neglecting the effects of surface tension we construct connected families of large amplitude periodic waves approaching a limiting wave, which is either a solitary wave, the highest solitary wave, the highest Stokes wave or a Stokes wave with a breaking profile. In particular, when the vorticity is nonnegative we prove the existence of highest Stokes waves with an included angle of 120 degrees. In contrast to previous studies, we fix the Bernoulli constant and consider the wavelength as a bifurcation parameter, which guarantees that the limiting wave has a finite depth. In fact, this is the first rigorous proof of the existence of extreme Stokes waves with vorticity on water of finite depth. Aside from the existence of highest waves, we provide a new result about the regularity of Stokes waves of arbitrary amplitude (including extreme waves). Furthermore, we prove several new facts about steady waves, such as a lower bound for the wavelength of Stokes waves, while also eliminating a possibility of the wave breaking for waves with non-negative vorticity., Funding Agencies|Swedish Research Council (VR) [2017-03837]

We consider a steady state heat conduction problem in a thin plate. In the application, it is used to connect two cylindrical containers and fix their relative positions. At the same time it serves to measure the temperature on the inner cylinder. We derive a two dimensional mathematical model, and use it to approximate the heat conduction in the thin plate. Since the plate has sharp edges on the sides the resulting problem is described by a degenerate elliptic equation. To find the temperature in the interior part from the exterior measurements, we formulate the problem as a Cauchy problem for stationary heat equation. We also reformulate the Cauchy problem as an operator equation, with a compact operator, and apply the Landweber iteration method to solve the equation. The case of the degenerate elliptic equation has not been previously studied in this context. For numerical computation, we consider the case where noisy data is present and analyse the convergence., Funding Agencies|Linkping University

We consider a steady state heat conduction problem in a thin plate. In the application, it is used to connect two cylindrical containers and fix their relative positions. At the same time it serves to measure the temperature on the inner cylinder. We derive a two dimensional mathematical model, and use it to approximate the heat conduction in the thin plate. Since the plate has sharp edges on the sides the resulting problem is described by a degenerate elliptic equation. To find the temperature in the interior part from the exterior measurements, we formulate the problem as a Cauchy problem for stationary heat equation. We also reformulate the Cauchy problem as an operator equation, with a compact operator, and apply the Landweber iteration method to solve the equation. The case of the degenerate elliptic equation has not been previously studied in this context. For numerical computation, we consider the case where noisy data is present and analyse the convergence.

Tumor cells with stem cell properties are considered to play major roles in promoting the development and malignant behavior of aggressive cancers. Therapeutic strategies that efficiently eradicate such tumor stem cells are of highest clinical need. Herein, we performed the validation of the polycationic phosphorus dendrimer-based approach for small interfering RNAs delivery in in vitro stem-like cells as models. As a therapeutic target, we chose Lyn, a member of the Src family kinases as an example of a prominent enzyme class widely discussed as a potent anti-cancer intervention point. Our selection is guided by our discovery that Lyn mRNA expression level in glioma, a class of brain tumors, possesses significant negative clinical predictive value, promoting its potential as a therapeutic target for future molecular-targeted treatments. We then showed that anti-Lyn siRNA, delivered into Lyn-expressing glioma cell model reduces the cell viability, a fact that was not observed in a cell model that lacks Lyn-expression. Furthermore, we have found that the dendrimer itself influences various parameters of the cells such as the expression of surface markers PD-L1, TIM-3 and CD47, targets for immune recognition and other biological processes suggested to be regulating glioblastoma cell invasion. Our findings prove the potential of dendrimer-based platforms for therapeutic applications, which might help to eradicate the population of cancer cells with augmented chemotherapy resistance. Moreover, the results further promote our functional stem cell technology as suitable component in early stage drug development.

We consider the Cauchy problem for the Helmholtz equation with a domain in R^d, d>2 with N cylindrical outlets to infinity with bounded inclusions in R^{d-1}. Cauchy data are prescribed on the boundary of the bounded domains and the aim is to find solution on the unbounded part of the boundary. In 1989, Kozlov and Maz'ya proposed an alternating iterative method for solving Cauchy problems associated with elliptic,self-adjoint and positive-definite operators in bounded domains. Different variants of this method for solving Cauchy problems associated with Helmholtz-type operators exists. We consider the variant proposed by Mpinganzima et al. for bounded domains and derive the necessary conditions for the convergence of the procedure in unbounded domains. For the numerical implementation, a finite difference method is used to solve the problem in a simple rectangular domain in R^2 that represent a truncated infinite strip. The numerical results shows that by appropriate truncation of the domain and with appropriate choice of the Robin parameters, the Robin-Dirichlet alternating iterative procedure is convergent., Comment: 7 figures,3 tables

The Cauchy problem for general elliptic equations of second order is considered. In a previous paper (Berntsson et al. in Inverse Probl Sci Eng 26(7):1062–1078, 2018), it was suggested that the alternating iterative algorithm suggested by Kozlov and Maz’ya can be convergent, even for large wavenumbers k2, in the Helmholtz equation, if the Neumann boundary conditions are replaced by Robin conditions. In this paper, we provide a proof that shows that the Dirichlet–Robin alternating algorithm is indeed convergent for general elliptic operators provided that the parameters in the Robin conditions are chosen appropriately. We also give numerical experiments intended to investigate the precise behaviour of the algorithm for different values of k2 in the Helmholtz equation. In particular, we show how the speed of the convergence depends on the choice of Robin parameters.

The Cauchy problem for general elliptic equations of second order is considered. In a previous paper (Berntsson et al. in Inverse Probl Sci Eng 26(7):1062–1078, 2018), it was suggested that the alternating iterative algorithm suggested by Kozlov and Maz’ya can be convergent, even for large wavenumbers k2, in the Helmholtz equation, if the Neumann boundary conditions are replaced by Robin conditions. In this paper, we provide a proof that shows that the Dirichlet–Robin alternating algorithm is indeed convergent for general elliptic operators provided that the parameters in the Robin conditions are chosen appropriately. We also give numerical experiments intended to investigate the precise behaviour of the algorithm for different values of k2 in the Helmholtz equation. In particular, we show how the speed of the convergence depends on the choice of Robin parameters.

We prove a comparison theorem for super- and sub-solutions with non-vanishing gradients to semilinear PDEs provided a nonlinearityfisL(p)function withp> 1. The proof is based on a strong maximum principle for solutions of divergence type elliptic equations with VMO leading coefficients and with lower order coefficients from a Kato class. An application to estimation of periodic water waves profiles is given., Funding Agencies|Swedish Research Council (VR)Swedish Research Council [EO418401]; Russian Foundation for Basic ResearchRussian Foundation for Basic Research (RFBR) [18-01-00472]

We prove a comparison theorem for super- and sub-solutions with non-vanishing gradients to semilinear PDEs provided a nonlinearityfisL(p)function withp> 1. The proof is based on a strong maximum principle for solutions of divergence type elliptic equations with VMO leading coefficients and with lower order coefficients from a Kato class. An application to estimation of periodic water waves profiles is given., Funding Agencies|Swedish Research Council (VR)Swedish Research Council [EO418401]; Russian Foundation for Basic ResearchRussian Foundation for Basic Research (RFBR) [18-01-00472]

In this paper we continue the stability analysis of the model for coinfection with density dependent susceptible population introduced in Andersson et al. (Effect of density dependence on coinfection dynamics. arXiv:2008.09987, 2020). We consider the remaining parameter values left out from Andersson et al. (Effect of density dependence on coinfection dynamics. arXiv:2008.09987, 2020). We look for coexistence equilibrium points, their stability and dependence on the carrying capacity K. Two sets of parameter value are determined, each giving rise to different scenarios for the equilibrium branch parametrized by K. In both scenarios the branch includes coexistence points implying that both coinfection and single infection of both diseases can exist together in a stable state. There are no simple explicit expression for these equilibrium points and we will require a more delicate analysis of these points with a new bifurcation technique adapted to such epidemic related problems. The first scenario is described by the branch of stable equilibrium points which includes a continuum of coexistence points starting at a bifurcation equilibrium point with zero single infection strain #1 and finishing at another bifurcation point with zero single infection strain #2. In the second scenario the branch also includes a section of coexistence equilibrium points with the same type of starting point but the branch stays inside the positive cone after this. The coexistence equilibrium points are stable at the start of the section. It stays stable as long as the product of K and the rate γ¯γ¯ of coinfection resulting from two single infections is small but, after this it can reach a Hopf bifurcation and periodic orbits will appear., Funding: Linkoping University

In this paper we continue the stability analysis of the model for coinfection with density dependent susceptible population introduced in Andersson et al. (Effect of density dependence on coinfection dynamics. arXiv:2008.09987, 2020). We consider the remaining parameter values left out from Andersson et al. (Effect of density dependence on coinfection dynamics. arXiv:2008.09987, 2020). We look for coexistence equilibrium points, their stability and dependence on the carrying capacity K. Two sets of parameter value are determined, each giving rise to different scenarios for the equilibrium branch parametrized by K. In both scenarios the branch includes coexistence points implying that both coinfection and single infection of both diseases can exist together in a stable state. There are no simple explicit expression for these equilibrium points and we will require a more delicate analysis of these points with a new bifurcation technique adapted to such epidemic related problems. The first scenario is described by the branch of stable equilibrium points which includes a continuum of coexistence points starting at a bifurcation equilibrium point with zero single infection strain #1 and finishing at another bifurcation point with zero single infection strain #2. In the second scenario the branch also includes a section of coexistence equilibrium points with the same type of starting point but the branch stays inside the positive cone after this. The coexistence equilibrium points are stable at the start of the section. It stays stable as long as the product of K and the rate γ¯γ¯ of coinfection resulting from two single infections is small but, after this it can reach a Hopf bifurcation and periodic orbits will appear., Funding: Linkoping University

In this paper we continue the stability analysis of the model for coinfection with density dependent susceptible population introduced in Andersson et al. (Effect of density dependence on coinfection dynamics. arXiv:2008.09987, 2020). We consider the remaining parameter values left out from Andersson et al. (Effect of density dependence on coinfection dynamics. arXiv:2008.09987, 2020). We look for coexistence equilibrium points, their stability and dependence on the carrying capacity K. Two sets of parameter value are determined, each giving rise to different scenarios for the equilibrium branch parametrized by K. In both scenarios the branch includes coexistence points implying that both coinfection and single infection of both diseases can exist together in a stable state. There are no simple explicit expression for these equilibrium points and we will require a more delicate analysis of these points with a new bifurcation technique adapted to such epidemic related problems. The first scenario is described by the branch of stable equilibrium points which includes a continuum of coexistence points starting at a bifurcation equilibrium point with zero single infection strain #1 and finishing at another bifurcation point with zero single infection strain #2. In the second scenario the branch also includes a section of coexistence equilibrium points with the same type of starting point but the branch stays inside the positive cone after this. The coexistence equilibrium points are stable at the start of the section. It stays stable as long as the product of K and the rate γ¯γ¯ of coinfection resulting from two single infections is small but, after this it can reach a Hopf bifurcation and periodic orbits will appear., Funding: Linkoping University

In this paper we continue the stability analysis of the model for coinfection with density dependent susceptible population introduced in Andersson et al. (Effect of density dependence on coinfection dynamics. arXiv:2008.09987, 2020). We consider the remaining parameter values left out from Andersson et al. (Effect of density dependence on coinfection dynamics. arXiv:2008.09987, 2020). We look for coexistence equilibrium points, their stability and dependence on the carrying capacity K. Two sets of parameter value are determined, each giving rise to different scenarios for the equilibrium branch parametrized by K. In both scenarios the branch includes coexistence points implying that both coinfection and single infection of both diseases can exist together in a stable state. There are no simple explicit expression for these equilibrium points and we will require a more delicate analysis of these points with a new bifurcation technique adapted to such epidemic related problems. The first scenario is described by the branch of stable equilibrium points which includes a continuum of coexistence points starting at a bifurcation equilibrium point with zero single infection strain #1 and finishing at another bifurcation point with zero single infection strain #2. In the second scenario the branch also includes a section of coexistence equilibrium points with the same type of starting point but the branch stays inside the positive cone after this. The coexistence equilibrium points are stable at the start of the section. It stays stable as long as the product of K and the rate γ¯γ¯ of coinfection resulting from two single infections is small but, after this it can reach a Hopf bifurcation and periodic orbits will appear., Funding: Linkoping University

We consider an age-structured density-dependent population model on several temporally variable patches. There are two key assumptions on which we base model setupand analysis. First, intraspecific competition is limited to competition between individuals of the same age (pure intra-cohort competition) and it affects density-dependentmortality. Second, dispersal between patches ensures that each patch can be reachedfrom every other patch, directly or through several intermediary patches, within individual reproductive age. Using strong monotonicity we prove existence and uniquenessof solution and analyze its large-time behavior in cases of constant, periodically variable and irregularly variable environment. In analogy to the next generation operator,we introduce the net reproductive operator and the basic reproduction number R0 fortime-independent and periodical models and establish the permanence dichotomy:if R0 ≤ 1, extinction on all patches is imminent, and if R0 > 1, permanence on allpatches is guaranteed. We show that a solution for the general time-dependent problemcan be bounded by above and below by solutions to the associated periodic problems. Using two-side estimates, we establish uniform boundedness and uniform persistenceof a solution for the general time-dependent problem and describe its asymptoticbehaviour, Funding: Linkoping University

In this paper we develop a compartmental model of SIR type (the abbreviation refers to the number of Susceptible, Infected and Recovered people) that models the population dynamics of two diseases that can coinfect. We discuss how the underlying dynamics depends on the carrying capacity K: from a simple dynamics to a more complex. This can also help in understanding the appearance of more complicated dynamics, for example, chaos and periodic oscillations, for large values of K. It is also presented that pathogens can invade in population and their invasion depends on the carrying capacity K which shows that the progression of disease in population depends on carrying capacity. More specifically, we establish all possible scenarios (the so-called transition diagrams) describing an evolution of an (always unique) locally stable equilibrium state (with only non-negative compartments) for fixed fundamental parameters (density independent transmission and vital rates) as a function of the carrying capacity K. An important implication of our results is the following important observation. Note that one can regard the value of K as the natural ‘size’ (the capacity) of a habitat. From this point of view, an isolation of individuals (the strategy which showed its efficiency for COVID-19 in various countries) into smaller resp. larger groups can be modelled by smaller resp. bigger values of K. Then we conclude that the infection dynamics becomes more complex for larger groups, as it fairly maybe expected for values of the reproduction number R0≈1. We show even more, that for the values R0>1 there are several (in fact four different) distinguished scenarios where the infection complexity (the number of nonzero infected classes) arises with growing K. Our approach is based on a bifurcation analysis which allows to generalize considerably the previous Lotka-Volterra model considered previously in Ghersheen et al. (Math Meth Appl Sci 42(8), 2019)., Funding: Swedish Research Council (VR)Swedish Research Council [2017-03837]

We prove the nonexistence of two-dimensional solitary gravity water waves with subcritical wave speeds and an arbitrary distribution of vorticity. This is a longstanding open problem, and even in the irrotational case there are only partial results relying on sign conditions or smallness assumptions. As a corollary, we obtain a relatively complete classification of solitary waves: they must be supercritical, symmetric, and monotonically decreasing on either side of a central crest. The proof introduces a new function which is related to the so-called flow force and has several surprising properties. In addition to solitary waves, our nonexistence result applies to "half-solitary" waves (e.g. bores) which decay in only one direction., Funding Agencies|Swedish Research Council (VR)Swedish Research Council [2017-03837]

In this paper we study prey-predator relationship in the presence of prey species pool. We describe the set of parameters when the predator will survive and find the threshold when you lose predator survival. This is based on analysis of dependence of locally stable equilibrium points on the parameters of the problem especially on the predator natural mortality rate e . In particular we give an interval for e in terms of other parameters where predators survive. This can allow to control the survival of predators by certain actions to move certain parameters to a safe area. We discover also a more complicated dynamics for small mortality rate. (C) 2021 Published by Elsevier B.V. on behalf of African Institute of Mathematical Sciences / Next Einstein Initiative., Funding Agencies|SIDA-UDSM capacity building programme

We consider an age-structured density-dependent population model on several temporally variable patches. There are two key assumptions on which we base model setupand analysis. First, intraspecific competition is limited to competition between individuals of the same age (pure intra-cohort competition) and it affects density-dependentmortality. Second, dispersal between patches ensures that each patch can be reachedfrom every other patch, directly or through several intermediary patches, within individual reproductive age. Using strong monotonicity we prove existence and uniquenessof solution and analyze its large-time behavior in cases of constant, periodically variable and irregularly variable environment. In analogy to the next generation operator,we introduce the net reproductive operator and the basic reproduction number R0 fortime-independent and periodical models and establish the permanence dichotomy:if R0 ≤ 1, extinction on all patches is imminent, and if R0 > 1, permanence on allpatches is guaranteed. We show that a solution for the general time-dependent problemcan be bounded by above and below by solutions to the associated periodic problems. Using two-side estimates, we establish uniform boundedness and uniform persistenceof a solution for the general time-dependent problem and describe its asymptoticbehaviour, Funding: Linkoping University

In this paper we study prey-predator relationship in the presence of prey species pool. We describe the set of parameters when the predator will survive and find the threshold when you lose predator survival. This is based on analysis of dependence of locally stable equilibrium points on the parameters of the problem especially on the predator natural mortality rate e . In particular we give an interval for e in terms of other parameters where predators survive. This can allow to control the survival of predators by certain actions to move certain parameters to a safe area. We discover also a more complicated dynamics for small mortality rate. (C) 2021 Published by Elsevier B.V. on behalf of African Institute of Mathematical Sciences / Next Einstein Initiative., Funding Agencies|SIDA-UDSM capacity building programme