Search

In this paper, we study the Cauchy problem of the two-species incompressible viscoelastic fluid of Oldroyd-B system, which involving a reaction effect between two species of polymers. We prove the local existence with initial data in Hk(k ≥ 2) in a classical solution framework, and then provide a blow-up criteria. We concentrate on the a priori estimate, by using the energy method. In particular, the variant system in a general formulation is also studied, and the corresponding local well-posedness is established. [ABSTRACT FROM AUTHOR]

We study the Cauchy problem of the new model of the three dimensional inertial nematic electrolyte, which models the N-species charged particles diffuse and advect in the nematic liquid crystalline matrix. This new model was proposed by [Calderer MC, Golovaty D, Lavrentovich O, et al. Modeling of nematic electrolytes and nonlinear electroosmosis. SIAM J Appl Math. 2016;76:2260–2285. doi: 10.1137/16M1056225]. The inertial effect is such that the system involves a hyperbolic feature. We first derive the local existence in large initial data when the flow is isotropy, i.e. $ \lambda =1 $ λ = 1. For the anisotropy case ( $ \lambda \gt 0 $ λ > 0 , $ \lambda \neq ~1 $ λ ≠ 1), we obtain small data local solutions. Then, by seeking some further dissipative mechanisms from the elliptic structures, the local solution can be extended globally near the constant states with electro-neutrality condition. [ABSTRACT FROM AUTHOR]

In this paper, we study the well‐posedness of the Cauchy problem to the compressible inertial Qian–Sheng model. Inspired by Jiang–Luo–Ma–Tang's work in [J. Hyperbolic. Differ. Equ 18:221‐256, 2021], we introduce a novel Condition (H) which ensures the energy dissipation, and then, we prove that when both the viscosity coefficients β5+β6=0$$ {\beta}_5&#x0002B;{\beta}_6&#x0003D;0 $$ and Condition (H) are satisfied, the local‐in‐time solutions exist for large initial data. Otherwise, we can only obtain small data local solutions. Finally, the local solution can be extended globally under at least one of the two conditions: (μ˜2−μ2)2<8β4μ1$$ {\left({\tilde{\mu}}_2-{\mu}_2\right)}&#x0005E;2<8{\beta}_4{\mu}_1 $$ or μ˜2=μ2$$ {\tilde{\mu}}_2&#x0003D;{\mu}_2 $$. [ABSTRACT FROM AUTHOR]

The doubly degenerate nutrient taxis model { u t = ∇ ⋅ (u v ∇ u) − ∇ ⋅ (S (u) v ∇ v) + ℓ u v , x ∈ Ω , t > 0 , v t = Δ v − u v , x ∈ Ω , t > 0 , is considered under no-flux boundary conditions in a bounded convex planar domain Ω with smooth boundary. It is firstly shown that within a general framework involving a conveniently large class of nonlinearities S , under an a priori assumption on regularity of solutions to certain approximate problems one can construct a global weak solution whose first component is uniformly bounded. Applications of this to particular settings thereafter reveal global existence of such bounded weak solutions when either S ∈ C 1 ([ 0 , ∞)) satisfies lim sup ξ → ∞ S (ξ) ξ α < ∞ with some α < 2 and the initial data (u 0 , v 0) are reasonably regular but arbitrary large, or S (ξ) = ξ 2 for ξ ≥ 0 and the initial data are such that v 0 satisfies an appropriate smallness condition. [ABSTRACT FROM AUTHOR]

In this article, we modify the results obtained by Mitidieri and Pohozhaev on sufficient conditions for the nonexistence of nontrivial weak solutions to nonlinear inequalities and systems with integer powers of the Laplace operator and with a nonlinear term of the form a(x) |∇(Δmu)|q + b(x)|∇u|s. We obtain optimal a priori estimates by applying the nonlinear capacity method with an appropriate choice of test functions. As a result, we prove the nonexistence of nontrivial weak solutions to nonlinear inequalities and systems by contradiction. [ABSTRACT FROM AUTHOR]

Accurate thermal infrared (TIR) fast-forward models are critical for weather forecasting via numerical weather prediction (NWP) satellite radiance assimilation and operational environmental data record (EDR) retrieval algorithms. The thermodynamic and compositional data about the surface and lower troposphere are derived from semi-transparent TIR window bands (i.e., surface-sensitive channels) that can span into the far-infrared (FIR) region under dry polar conditions. To model the satellite observed radiance within these bands, an accurate a priori emissivity is necessary for the surface in question, usually provided in the form of a physical or empirical model. To address the needs of hyperspectral TIR satellite radiance assimilation, this paper discusses the research, development, and preliminary validation of a physically based snow/ice emissivity model designed for practical implementation within operational fast-forward models such as the U.S. National Oceanic and Atmospheric Administration (NOAA) Community Radiative Transfer Model (CRTM). To accommodate the range of snow grain sizes, a hybrid modeling approach is adopted, combining a layer scattering model based on the Mie theory (viz., the Wiscombe–Warren 1980 snow albedo model, its complete derivation provided in the Appendices) with a specular facet model. The Mie-scattering model is valid for the smallest snow grain sizes typical of fresh snow and frost, whereas the specular facet model is better suited for the larger sizes and welded snow surfaces typical of aged snow. Comparisons of the model against the previously published spectral emissivity measurements show reasonable agreement across zenith observing angles and snow grain sizes, and preliminary observing system experiments (OSEs) have revealed notable improvements in snow/ice surface window channel calculations versus hyperspectral TIR satellite observations within the NOAA NWP radiance assimilation system. [ABSTRACT FROM AUTHOR]

For a certain class of second-order hyperbolic systems, a mixed problem with Dirichlet and Poincaré boundary conditions is studied. In the linear case, an explicit representation of a soultion of this problem is given and questions related to its uniqueness and existence are studied depending on the character of nonlinearities in the system. [ABSTRACT FROM AUTHOR]

We approximate the solution of the stream function formulation of the Oseen equations on general domains by designing a nonconforming Morley-type virtual element method. Under a suitable assumption on the continuous problem's coefficients, the discrete scheme is well-posed. By introducing an enriching operator, we derive an a priori estimate of the error in a discrete H2 norm. By post-processing the discrete stream function, we compute the discrete velocity and vorticity fields. Furthermore, we recover an approximate pressure field by solving a Stokes-like problem in a nonconforming Crouzeix–Raviart-type virtual element space that is in a Stokes-complex relation with the Morley-type space of the virtual element approximation. Finally, we confirm our theoretical estimates by solving benchmark problems that include a convex and a nonconvex domain. [ABSTRACT FROM AUTHOR]

We are devoted to the study of a non-local non-homogeneous time fractional Timoshenko system with frictional and viscoelastic damping terms. We are concerned with the well-posedness of the given problem. The approach relies on some functional analysis tools, operator theory, a priori estimates and density arguments. This work can be considered as a contribution to the development of energy inequality methods, the so-called a priori estimate method inspired from functional analyses and used to prove the well-posedness of mixed problems with integral boundary conditions. [ABSTRACT FROM AUTHOR]

The paper describes an interpolation method for obtaining a priori estimates for strong solutions of semilinear parabolic equations with unbounded singularities on the right-hand side, provided that there is a first a priori estimate in the space of summable functions. [ABSTRACT FROM AUTHOR]

New results on the strong solvability in Sobolev spaces of the quasilinear Venttsel' problem for parabolic equations with discontinuous leading coefficients are obtained. [ABSTRACT FROM AUTHOR]

This paper is concerned with the migration–consumption taxis system involving signal-dependent motilities u t = Δ (u m ϕ (v)) , v t = Δ v - u v , (∗) in smoothly bounded domains Ω ⊂ R n , where m > 1 and n ≥ 2 . It is shown that if ϕ ∈ C 3 ([ 0 , ∞)) is strictly positive on [ 0 , ∞) , for all suitably regular initial data an associated no-flux type initial-boundary value problem possesses a globally defined bounded weak solution, provided m > n 2 , which is consistent with the restriction imposed on m in corresponding signal production counterparts of (⋆) so as to establish the similar result. [ABSTRACT FROM AUTHOR]

This paper considers a theoretical substantiation of the influence of a perturbation of a moving singular point on the analytical approximate solution to the Van der Pol equation obtained earlier by the author. A priori estimates of the error of the analytical approximate solution are obtained, which allows the solving of the inverse problem of the theory of error: what should the structure of the analytical approximate solution be in order to obtain a result with a given accuracy? Thanks to a new approach for obtaining a priori evaluations of errors, based on elements of differential calculus, the domain, used to obtain an analytical approximate solution, was substantially expanded. A variant of optimizing a priori estimates using a posteriori estimates is illustrated. The results of a numerical experiment are also presented. [ABSTRACT FROM AUTHOR]

In this paper, for the mixed Navier—Stokes/Darcy model with Beavers—Joseph—Saffman's interface condition, we first establish an a priori estimate for possible weak solutions by means of expanding the coupled system. Then we prove the existence of weak solutions without the small data and/or large viscosity restriction, which is required for the existence of the weak solutions in literatures. As a direct corollary, we also get the global uniqueness of the weak solution. [ABSTRACT FROM AUTHOR]

The aim of this paper is to derive a novel discrete form of stochastic fractional Grönwall lemma involving a martingale. The proof of the derived inequality is accomplished by a corresponding no randomness form of the discrete fractional Grönwall inequality and an upper bound for discrete-time martingales representing the supremum in terms of the infimum. The release of a martingale term on the right-hand side of the given inequality and the graded L1 difference formula for the time Caputo fractional derivative of order 0 < α < 1 on the left-hand side are the main challenges of the stated and proved main theorem. As an example of application, the constructed theorem is used to derive an a priori estimate for a discrete stochastic fractional model at the end of the paper. [ABSTRACT FROM AUTHOR]

The existence of a weak solution to the initial boundary value problem for the equations of motion of a viscoelastic fluid with memory along the trajectories of a nonsmooth velocity field with inhomogeneous boundary condition is proved. The analysis involves Galerkin-type approximations of the original problem followed by the passage to the limit based on a priori estimates. To study the behavior of trajectories of a nonsmooth velocity field, the theory of regular Lagrangian flows is used. [ABSTRACT FROM AUTHOR]

The article considers the Van der Pol equation nonlinearity aspect related to a moving singular point. The fact of the existence of moving singular points and the uniqueness of their solution for complex domains have been proved. An answer to the question about the existence of moving singular points in the real domain was obtained. The proof of existence and uniqueness is based on an author's modification of the technology of the classical Cauchy theorem. A priori estimates of the analytical approximate solution in the vicinity of a moving singular point are obtained. Calculations of a numerical experiment are presented. [ABSTRACT FROM AUTHOR]

In this article, we consider the kinetic derivative nonlinear Schrödinger equation (KDNLS), which is a one-dimensional nonlinear Schrödinger equation with a cubic derivative nonlinear term containing the Hilbert transformation. For the Cauchy problem, both on the real line and on the circle, we apply the short-time Fourier restriction method to establish a priori estimate for small and smooth solutions in Sobolev spaces H s with s > 1 / 4 . [ABSTRACT FROM AUTHOR]

The parabolic problem u t = Δ (u ϕ (v)) , v t = Δ v - u v , is considered in smoothly bounded subdomains of R n with arbitrary n ≥ 1 . Under the assumptions that ϕ ∈ C 0 ([ 0 , ∞)) ∩ C 3 ((0 , ∞)) is positive on (0 , ∞) and satisfies lim inf ξ ↘ 0 ϕ (ξ) ξ α > 0 and lim sup ξ ↘ 0 { ξ β | ϕ ′ (ξ) | } < ∞ with some α > 0 and β > 0 , for all reasonably regular initial data an associated no-flux type initial-boundary value problem is shown to admit a global solution in an appropriately generalized sense. This extends previously developed solution theories on problems of this form, which either concentrated on non-degenerate or weakly degenerate cases corresponding to the choices α = 0 and α ∈ (0 , 2) , or were restricted to low-dimensional settings by requiring that n ≤ 2 . [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence and uniqueness of Caputo time fractional pseudo-hyperbolic equations of higher order with purely nonlocal conditions of integral type. We use an a priori estimate method; the so-called energy inequalities method, based on some functional analysis tools, is developed for a Caputo time fractional of 2 ⁢ m -th and (2 ⁢ m + 1) -th order and the density of the range of the operator generated by the considered problem. Using the Laplace transform and homotopy perturbation, we find a semi-analytical solution. Finally, we give some examples for illustration. [ABSTRACT FROM AUTHOR]

The Degasperis-Procesi (DP) equation is an integrable Camassa-Holm-type model which is an asymptotic approximation for the unidirectional propagation of shallow water waves. This work establishes the orbital stability of localized smooth solitary waves to the DP equation on the real line, extending our previous work on their spectral stability [J. Math. Pures Appl. (9) 142 (2020), pp. 298–314]. The main difficulty stems from the fact that the natural energy space is a subspace of L^3, but the translation symmetry for the DP equation gives rise to a conserved quantity equivalent to the L^2-norm, resulting in L^3 higher-order nonlinear terms in the augmented Hamiltonian. But the usual coercivity estimate is in terms of L^2 norm for DP equation, which cannot be used to control the L^3 higher order term directly. The remedy is to observe that, given a sufficiently smooth initial condition satisfying some mild constraint, the L^\infty orbital norm of the perturbation is bounded above by a function of its L^2 orbital norm, yielding the higher order control and the orbital stability in the L^2\cap L^\infty space. [ABSTRACT FROM AUTHOR]

In this paper, we prove coercive a priori estimates of solutions of a Dirichlet-type boundary-value problem in a strip for a certain higher-order degenerate elliptic equation containing weighted derivatives of a special form up to the order 2m and ordinary partial derivatives up to the order 2k−1 under the condition 2m > 2k −1. At the boundary of the strip, Dirichlet-type conditions are imposed. A coercive a priori estimate for solutions of the problem considered in special weighted Sobolev-type spaces is obtained. [ABSTRACT FROM AUTHOR]

We study traveling wave solutions for a two-species non-local diffusive system. This paper is inspired by the importance of biological non-local dispersal to biologists for data collection (Lee in J Theor Biol 210(2):210-219, 2001). We also consider the bistable nonlinearities in the Lotka-Volterra system. We construct an N-shaped constrained region, and then maximum principle is applied to this non-local system. Finally, we use this N-barrier maximum principle (NBMP) (Chen, Hsiao and Hung in Discrete Contin Dyn Syst 41(1):153, 2020. Chen and Hung in J Differ Equ 261(8):4573–4592, 2016a. Chen and Hung in Commun Pure Appl Anal 15(4):1451, 2016b. Chen and Hung in Discrete Contin Dyn Syst - B, 2018. Chen, Hung and Lai in Commun Pure Appl Anal 18(1):33, 2019. Chen, Hung and Liu in Discrete Contin Dyn Syst A 38(2):791–821, 2018. Hung and Liao in Jpn J Ind Appl Math 37(3):819–830, 2020) to give an a priori estimate for this system and show that the total population mass of this system has a non-trivial lower bound. [ABSTRACT FROM AUTHOR]

In this paper, we consider the boundary value problem for one class of higher-order semilinear hyperbolic systems. We prove the theorems on the existence, uniqueness, and nonexistence of solutions of this problem. [ABSTRACT FROM AUTHOR]

We study the steady Boltzmann equation in half-space, which arises in the Knudsen boundary layer problem, with diffusive reflection boundary conditions. Under certain admissible conditions, we establish the existence of a boundary layer solution for both linear and nonlinear Boltzmann equations in half-space with diffusive reflection boundary condition in L∞x,v when the far-field Mach number of the Maxwellian is zero. The continuity and the special decay of the solution are obtained. The uniqueness is established under some constraint conditions. [ABSTRACT FROM AUTHOR]

The paper considers the specifics of nonlinear differential equations that have applications in different areas. Earlier, the authors proved the existence and uniqueness theorem for a solution to a class of non-linear differential equations in a neighborhood of a moving singular point. In this paper, we consider the first problem of studying a third-order nonlinear differential equation in the domain of analyticity. An analytical approximate solution is built, taking into account the solution search area. A priori estimates of the analytical approximate solution are obtained, and the technology of their optimization using a posteriori ones is illustrated. The result of a numerical experiment is presented. The presented results allow to expand the class of nonlinear differential equations for describing various phenomena and processes. [ABSTRACT FROM AUTHOR]

This paper deals with the initial value problem for a parabolic attraction-repulsion chemotaxis system in R 2 : { ∂ t u = Δ u − ∇ ⋅ (u ∇ (β 1 v 1 − β 2 v 2)) , t > 0 , x ∈ R 2 , ∂ t v j = Δ v j − λ j v j + u , t > 0 , x ∈ R 2 (j = 1 , 2) , u (0 , x) = u 0 (x) , v j (0 , x) = v j 0 (x) , x ∈ R 2 (j = 1 , 2) with positive parameters β 1 , β 2 , λ 1 , λ 2 and nonnegative initial data u 0 , v 10 , v 20. It is well known that the sign of β 1 − β 2 and the mass on u 0 play a crucial role in the global boundedness of the system. Specifically, in the attractive dominant case β 1 > β 2 , the uniform boundedness of nonnegative solutions has been guaranteed under the condition ∫ R 2 u 0 d x < 4 π. Also, in the balance case β 1 = β 2 , it has been proven that every nonnegative solution is bounded uniformly in time without any restriction on the mass u 0. In this paper, we discuss the global existence and boundedness of nonnegative solutions to the system in the repulsive dominant case β 1 < β 2. [ABSTRACT FROM AUTHOR]

We investigate Monge–Ampère type fully nonlinear equations on compact almost Hermitian manifolds with boundary and show a priori gradient estimates for a smooth solution of these equations. [ABSTRACT FROM AUTHOR]

In this paper, a boundary-value problem for the inhomogeneous Aller–Lykov moisture transfer equation with a fractional Riemann–Liouville time derivative is examined. The equation considered is a generalization of the Aller–Lykov equation obtained by introducing the fractal rate of change of humidity, which explains the appearance of flows directed against the potential of humidity. The existence of a solution to the first boundary-value problem is proved by the Fourier method. Using the method of energy inequalities for solutions of the problem, we obtain an a priori estimate in terms of the fractional Riemann–Liouville derivative, which implies the uniqueness of the solution. [ABSTRACT FROM AUTHOR]

In this paper, a theorem on a priori estimates of solutions of the Tricomi problem for a second-order, mixed-type equation with the Gellerstedt operator in the hyperbolicity domain is proved. The a priori estimate obtained implies the uniqueness of the regular solution of the problem considered. [ABSTRACT FROM AUTHOR]

In this paper we study the Neumann problem for a type of fully nonlinear second order elliptic partial differential equations on domains in C n without any curvature assumptions on the domain. [ABSTRACT FROM AUTHOR]

In this paper, weestablish global C2 estimates for a class of mixed Hessian equations with the Neumann boundary condition and obtain the existence theorem of k‐admissible solutions for the classical Neumann problem of these mixed Hessian equations. [ABSTRACT FROM AUTHOR]

In this article, we study closed star-shaped (n, k)-convex hyper-surfaces in space forms satisfying a class of k-Hessian curvature type equations. Firstly, using the maximum principle, we obtain a priori estimates for the class of Hessian curvature type equations. Secondly, we obtain an existence result by using standard degree theory based on a priori estimates. [ABSTRACT FROM AUTHOR]

In this article we investigate an ill-posed problem for the system of inhomogeneous equations of parabolic type with changing the direction of time. We obtained an a priori estimate based on the given data. The theorems of uniqueness and conditional stability are proved on the set of correctness of the solution. An approximate solution to the problem is constructed by the regularization method. We calculate an estimate for efficiency of the norm of the difference between exact and approximate solutions. [ABSTRACT FROM AUTHOR]

This paper studies the asymptotic behavior of coexistence steady-states of the Shigesada-Kawasaki-Teramoto model as both cross-diffusion coefficients tend to infinity at the same rate. In the case when either one of two cross-diffusion coefficients tends to infinity, Lou and Ni [18] derived a couple of limiting systems, which characterize the asymptotic behavior of coexistence steady-states. Recently, a formal observation by Kan-on [10] implied the existence of a limiting system including the nonstationary problem as both cross-diffusion coefficients tend to infinity at the same rate. This paper gives a rigorous proof of his observation as far as the stationary problem. As a key ingredient of the proof, we establish a uniform L ∞ estimate for all steady-states. Thanks to this a priori estimate, we show that the asymptotic profile of coexistence steady-states can be characterized by a solution of the limiting system. [ABSTRACT FROM AUTHOR]

We study the free boundary problem with no initial conditions for a third-order relaxation transfer equation. First, we reduce the problem to a second-order equation and prove the uniqueness theorem. The solution of this problem is constructed as a limit of solutions of corresponding problems that are first reduced to a Stefan-type problem with initial conditions. Free boundary behavior is explored. [ABSTRACT FROM AUTHOR]

We present a coupling of the Finite Element and the Boundary Element Method in an isogeometric framework to approximate either two-dimensional Laplace interface problems or boundary value problems consisting of two disjoint domains. We consider the Finite Element Method in the bounded domains to simulate possibly non-linear materials. The Boundary Element Method is applied in unbounded or thin domains where the material behavior is linear. The isogeometric framework allows to combine different design and analysis tools: first, we consider the same type of NURBS parameterizations for an exact geometry representation and second, we use the numerical analysis for the Galerkin approximation. Moreover, it facilitates to perform h- and p-refinements. For the sake of analysis, we consider the framework of strongly monotone and Lipschitz continuous operators to ensure well-posedness of the coupled system. Furthermore, we provide a priori error estimates. We additionally show an improved convergence behavior for the errors in functionals of the solution that may double the rate under certain assumptions. Numerical examples conclude the work which illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper focusses on the von Kármán equations for the moderately large deformation of a very thin plate with the convex obstacle constraint leading to a coupled system of semilinear fourth-order obstacle problem and motivates its nonconforming Morley finite element approximation. The first part establishes the well-posedness of the von Kármán obstacle problem and also discusses the uniqueness of the solution under an a priori and an a posteriori smallness condition on the data. The second part of the article discusses the regularity result of Frehse from 1971 and combines it with the regularity of the solution on a polygonal domain. The third part of the article shows an a priori error estimate for optimal convergence rates for the Morley finite element approximation to the von Kármán obstacle problem for small data. The article concludes with numerical results that illustrates the requirement of smallness assumption on the data for optimal convergence rate. [ABSTRACT FROM AUTHOR]

In this paper, we establish the global-in-time hydrodynamic limit of the Boltzmann equation to the planar rarefaction wave of a compressible Euler system in three dimensional space x ∈ ℝ³ for general collision kernels. Our approach is based on the Hilbert expansion and a recent L²-L∞ framework. In particular, we improve the L²-estimate to be a localized version because the planar rarefaction wave is indeed a one dimensional wave which makes the source terms not integrable in the L² energy estimate of the three dimensional problem. We also point out that the wave strength of rarefaction may be large. [ABSTRACT FROM AUTHOR]

This paper is concerned with the second-order nonlinear Robin problem involving the first-order derivative: { u ″ + f (t , u , u ′) = 0 , u (0) = u ′ (1) − α u (1) = 0 , where f ∈ C ([ 0 , 1 ] × R + 2 , R +) and α ∈ ] 0 , 1 [ . Based on a priori estimates, we use fixed point index theory to establish some results on existence, multiplicity and uniqueness of positive solutions thereof, with the unique positive solution being the limit of of an iterative sequence. The results presented here generalize and extend the corresponding ones for nonlinearities independent of the first-order derivative. [ABSTRACT FROM AUTHOR]

We demonstrate some a priori estimates of a scheme using stabilization and hybrid interfaces applying to partial differential equations describing miscible displacement in porous media. This system is made of two coupled equations: an anisotropic diffusion equation on the pressure and a convection-diffusion-dispersion equation on the concentration of invading fluid. The anisotropic diffusion operators in both equations require special care while discretizing by a finite volume method SUSHI. Later, we present some numerical experiments. [ABSTRACT FROM AUTHOR]

In this article,we investigate an initial and boundary value problem for a class of compressible non-Newtonian fluids, provided the initial energy is small and the initial density containing the vacuum state is allowed. For p > 2, we obtain the existence and uniqueness of the global strong solution for this problem in a one-dimensional bounded interval. [ABSTRACT FROM AUTHOR]

In real‐world applications the perspective‐n‐point (PnP) problem should generally be applied to a sequence of images which a set of drift‐prone features are tracked over time. In this study, the authors consider both the temporal dependency of camera poses and the uncertainty of features for the vision‐only sequential camera pose estimation. Using the extended Kalman filter (EKF), a priori estimate of the camera pose is calculated from the camera motion model and then it is corrected by minimising the reprojection error of the reference points. Applying probabilistic approach also provides the covariance of the pose parameters which helps to measure the reliability of the estimated parameters. Experimental results, using both synthetic and real data, demonstrate that the proposed method improves the robustness of the camera pose estimation, in the presence of tracking error and feature matching outliers, compared to the state of the art. [ABSTRACT FROM AUTHOR]

In real-world applications the perspective-n-point (PnP) problem should generally be applied to a sequence of images which a set of drift-prone features are tracked over time. In this study, the authors consider both the temporal dependency of camera poses and the uncertainty of features for the vision-only sequential camera pose estimation. Using the extended Kalman filter (EKF), a priori estimate of the camera pose is calculated from the camera motion model and then it is corrected by minimising the reprojection error of the reference points. Applying probabilistic approach also provides the covariance of the pose parameters which helps to measure the reliability of the estimated parameters. Experimental results, using both synthetic and real data, demonstrate that the proposed method improves the robustness of the camera pose estimation, in the presence of tracking error and feature matching outliers, compared to the state of the art. [ABSTRACT FROM AUTHOR]

A nonlocal wave equation with variable coefficients in a rectangular domain is considered. The first and third boundary-value problems in the differential form are examined; the method of lines in the difference form is applied for solving these problems. For the system of difference equations with constant coefficients arising from the method of lines, a solution is obtained. [ABSTRACT FROM AUTHOR]

We consider a system for a generalized Schnakenberg model, showing Turing pattern formation for a wide class of nonlinearities. [ABSTRACT FROM AUTHOR]