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This paper deals with an adaptation of the Poincare-Lindstedt method for the determination of periodic orbits in three-dimensional nonlinear differential systems. We describe here a general symbolic algorithm to implement the method and apply it to compute periodic solutions in a three-dimensional Lotka-Volterra system modeling a chain food interaction. The sufficient conditions to make secular terms disappear from the approximate series solution are given in the paper.

In this paper we investigate a time dependent family of plane closed Jordan curves evolving in the normal direction with a velocity which is assumed to be a function of the curvature, tangential angle and position vector of a curve. We follow the direct approach and analyze the system of governing PDEs for relevant geometric quantities. We focus on a class of the so-called curvature adjusted tangential velocities for computation of the curvature driven flow of plane closed curves. Such a curvature adjusted tangential velocity depends on the modulus of the curvature and its curve average. Using the theory of abstract parabolic equations we prove local existence, uniqueness and continuation of classical solutions to the system of governing equations. We furthermore analyze geometric flows for which normal velocity may depend on global curve quantities like the length, enclosed area or total elastic energy of a curve. We also propose a stable numerical approximation scheme based on the flowing finite volume method. Several computational examples of various nonlocal geometric flows are also presented in this paper., submitted to MMAS

This paper is concerned with computable and guaranteed upper bounds of the difference between exact solutions of variational inequalities arising in the theory of viscous fluids and arbitrary approximations in the corresponding energy space. Such estimates (also called error majorants of functional type) have been derived for the considered class of nonlinear boundary-value problems in (Math. Meth. Appl. Sci. 2006; 29:2225–2244) with the help of variational methods based on duality theory from convex analysis. In the present paper, it is shown that error majorants can be derived in a different way by certain transformations of the variational inequalities that define generalized solutions. The error bounds derived by this techniques for the velocity function differ from those obtained by the variational method. These estimates involve only global constants coming from Korn- and Friedrichs-type inequalities, which are not difficult to evaluate in case of Dirichlet boundary conditions. For the case of mixed boundary conditions, we also derive another form of the estimate that contains only one constant coming from the following assertion: the L2 norm of a vector-valued function from H1(Ω) in the factor space generated by the equivalence with respect to rigid motions is bounded by the L2 norm of the symmetric part of the gradient tensor. As for some ‘simple’ domains such as squares or cubes, the constants in this inequality can be found analytically (or numerically), we obtain a unified form of an error majorant for any domain that admits a decomposition into such subdomains. Copyright © 2009 John Wiley & Sons, Ltd.

SUMMARY 9 In this paper we investigate the unknown body problem in a wave guide where one boundary has a pressure release condition and the other an impedance condition. The method used in the paper for 11 solving the unknown body inverse problem is the intersection canonical body approximation (ICBA). The ICBA is based on the Rayleigh conjecture, which states that every point on an illuminated body 13 radiates sound from that point as if the point lies on its tangent sphere. The ICBA method requires that an analytical solution be known exterior to a canonical body in the wave guide. We use the sphere of 15 arbitrary centre and radius in the wave guide as our canonical body. We are lead then to analytically computing the exterior solution for a sphere between two parallel plates. We use the ICBA to construct 17 solutions at points ranging over the suspected surface of the unknown object to reconstruct the unknown

We study the process of two-phase flow in thin porous media domains of Brinkman-type. This is generally described by a model of coupled, mixed-type differential equations of fluids' saturation and pressure. To reduce the model complexity, different approaches that utilize the thin geometry of the domain have been suggested. We focus on a reduced model that is formulated as a single nonlocal evolution equation of saturation. It is derived by applying standard asymptotic analysis to the dimensionless coupled model, however, a rigid mathematical derivation is still lacking. In this paper, we prove that the reduced model is the analytical limit of the coupled two-phase flow model as the geometrical parameter of domain's width--length ratio tends to zero. Precisely, we prove the convergence of weak solutions for the coupled model to a weak solution for the reduced model as the geometrical parameter approaches zero.

This paper is concerned with a parabolic-elliptic Keller-Segel system where both diffusive and chemotactic coefficients (motility functions) depend on the chemical signal density. This system was originally proposed by Keller and Segel in \cite{KS-1971-JTB2} to describe the aggregation phase of {\it Dictyostelium discoideum} cells in response to the secreted chemical signal cyclic adenosine monophosphate (cAMP), but the available analytical results are very limited by far. Considering system in a bounded smooth domain with Neumann boundary conditions, we establish the global boundedness of solutions in any dimensions with suitable general conditions on the signal-dependent motility functions, which are applicable to a wide class of motility functions. The existence/nonexistence of non-constant steady states is studied and abundant stationary profiles are found. Some open questions are outlined for further pursues. Our results demonstrate that the global boundedness and profile of stationary solutions to the Keller-Segel system with signal-dependent motilities depend on the decay rates of motility functions, space dimensions and the relation between the diffusive and chemotactic motilities, which makes the dynamics immensely wealthy.

In this paper, we establish existence and finite time blow up of weak solutions of a parabolic equation of p(x)-Laplacian type with the Dirichlet boundary condition. Moreover, we obtain upper and lower bounds for the blow up time of solutions, by employing concavity method and differential inequality technique respectively.

We consider singularly perturbed convection-diffusion equations on one-dimensional networks (metric graphs) as well as the transport problems arising in the vanishing diffusion limit. Suitable coupling condition at inner vertices are derived that guarantee conservation of mass as well as dissipation of a mathematical energy which allows us to prove stability and well-posedness. For single intervals and appropriately specified initial conditions, it is well-known that the solutions of the convection-diffusion problem converge to that of the transport problem with order $O(\sqrt{\epsilon})$ in the $L^\infty(L^2)$-norm with diffusion $\epsilon \to 0$. In this paper, we prove a corresponding result for problems on one-dimensional networks. The main difficulty in the analysis is that the number and type of coupling conditions changes in the singular limit which gives rise to additional boundary layers at the interior vertices of the network. Since the values of the solution at these network junctions are not known a-priori, the asymptotic analysis requires a delicate choice of boundary layer functions that allows to handle these interior layers.

In this paper, we consider the Cauchy problem for three-dimensional isentropic compressible radiation hydrodynamic equations with density-dependent viscosity coefficients. When the viscosity coefficients are given as power of density ($\rho^\delta$ with $\delta>1$), we establish the local-in-time existence of classical solutions containing a vacuum for large initial data. Here, we point out that the initial layer compatibility conditions are not necessary.

In this paper, the authors obtain some new blow up criteria for the smooth solution to the three dimensional magnetic B\’enard equation without thermal diffusion in terms of pressure. We prove that if $\pi\in L^2(0, T; L^{\f3r}(\R^3))$ with $0

The paper deals with the analysis of stable thermo-solutal dendritic growth in the presence of intense convection. The n-fold symmetry of crystalline anisotropy as well as the two- and three-dimensional growth geometries are considered. The steady-state analytical solutions are found with allowance for the convective-type heat and mass exchange boundary conditions at the dendritic surface. A linear morphological stability analysis determining the marginal wavenumber is carried out. The new stability criterion is derived from the solvability theory and stability analysis. This selection criterion takes place in the regions of small undercooling. To describe a broader undercooling diapason, the obtained selection criterion, which describes the case of intense convection, is stitched together with the previously known selection criterion for the conductive-type boundary conditions. It is demonstrated that the stitched selection criterion well describes a broad diapason of experimental undercoolings.

The aim of this paper is to investigate the global dynamics of the delay nonlinear difference equation (Formula presented.) where k, l, and m are positive integers, the parameters A, B, C, p, and q are nonnegative real numbers, and the initial values (Formula presented.) are nonnegative real numbers such that the denominator is always positive. Several numerical simulations are provided to support obtained results. Also, our results extend and generalize the known ones. © 2019 John Wiley & Sons, Ltd., The author would like to thank the editor and the anonymous referees for their careful reading and constructive suggestions. This work is financially supported by TUBITAK. The founding sponsor had no role in the writing of the article and in the decision to publish the results.

In this paper, we prove the global existence of the weak solution to the mean field kinetic equation derived from the $N$-particle Newtonian system. For $L^1\cap L^\infty$ initial data, the solvability of the mean field kinetic equation can be obtained by using uniform estimates and compactness arguments while the difficulties arising from the non-local non-linear interaction are tackled appropriately using the Aubin-Lions compact embedding theorem.

In this paper we study the stability of a tree-shaped network of elastic strings and beams with some feedbacks at the ends. The whole system is asymptotically stable. Moreover, the energy of the solution decay exponentially to zero if there is no beam following a string ( from the root to the leaves) and decay polynomially if not. We use a frequency domain method from the semigroups theory.

In this paper, we establish a small time large deviation principle for the strong solution of 3D stochastic primitive equations driven by multiplicative noise. Both the small noise and the small, but highly nonlinear, unbounded nonlinear terms should be taken into consideration.

In this paper, the mathematical modeling and trajectory planning of a 3D rotating manipulator composed of a rotating-prismatic joint and multiple rigid links is considered. Possible trajectories of the end effector of the manipulator—following a sequence of 3D target points under the action of 2 external driving torques and an axial force—are modeled using zenithal gnomic projections and polar piecewise interpolants expressed as polynomial Hermite-type functions. Because of the geometry of the manipulator, the time-dependent generalized coordinates are associated with the spherical coordinates named the radial distance related to the manipulator length, and the polar and azimuthal angles describing the left and right and, respectively, up and down motion of the manipulator. The polar trajectories (left and right motion) of the end effector are generated using a inverse geometric transformation applied to the polar piecewise interpolants that approximate the gnomic projective trajectory of the 3D via-points. The gnomic via-points—located on a projective plane situated on the northern hemisphere—are seen from the manipulator base location, which represents the center of rotation of the extensible manipulator. The related azimuthal trajectory (up and down motion) is generated by polar piecewise interpolants on the azimuthal angles. Smoothness of the polygonal trajectory is obtained through the use of piecewise interpolants with continuous derivatives, while the kinematics and dynamics implementation of the model is well suited to computer implementation (easy calculation of kinematics variables) and simulation. To verify the approach and validate the model, a numerical example—implemented in Matlab—is presented, and the results are discussed.

In this paper, we obtain optimal decay estimates for the solutions to an evolution equation with critical, structural, dissipation, and absorbing power nonlinearity: utt+Δ2θu+2μ(−Δ)θut+|ut|p−1ut=0,t≥0,x∈Rn, with μ>0, θ is a positive integer, and p>1+4θ/n, in space dimension n∈(2θ,4θ). We use these estimates to find the self-similar asymptotic profile of the solutions, when μ≥1.

This paper addresses the analysis of a time noise‐driven Allen-Cahn equation modelling the evolution of damage in continuum media in the presence of stochastic dynamics. The nonlinear character of the equation is mainly due to a multivoque maximal monotone operator representing a constraint on the damage variable, which is forced to take physically admissible values. By a Yosida approximation and a time‐discretization procedure, we prove a result of global‐in‐time existence and uniqueness of the solution to the stochastic problem.

In this paper we consider the inviscid limit for the periodic solutions to Navier-Stokes equation in the framework of Gevrey class. It is shown that the lifespan for the solutions to Navier-Stokes equation is independent of viscosity, and that the solutions of the Navier-Stokes equation converge to that of Euler equation in Gevrey class as the viscosity tends to zero. Moreover the convergence rate in Gevrey class is presented.

In this paper, we consider the 2D incompressible Boussinesq system with fractional Laplacian dissipation and thermal diffusion. On the basis of the previous works and some new observations, we show that the condition 1−α

In this paper, we study the acoustic properties of porous media saturated by an incompressible viscoelastic fluid. The model considered here consists of a linear deformable porous skeleton having memory that is surrounded by a viscoelastic Oldroyd fluid. Assuming the microstructures to be almost periodically distributed and under the almost periodicity hypothesis on the coefficients of the governing equations, we determine the macroscopic equivalent medium. To achieve our goal, we use some very recent tools about the sigma convergence of convolution sequences. Copyright © 2017 John Wiley & Sons, Ltd.

In this paper, we discuss with the global well-posedness of 2D anisotropic nonlinear Boussinesq equations with any two positive viscosities and one positive thermal diffusivity. More precisely, for three kinds of viscous combinations, we obtain the global well-posedness without any assumption on the solution. For other three difficult cases, under the minimal regularity assumption, we also derive the unique global solution. To the authors' knowledge, our result is new even for the simplified model, that is, F(θ) = θe2. Copyright © 2017 John Wiley & Sons, Ltd.

In this paper, we consider the conductivity problem with piecewise-constant conductivity and Robin-type boundary condition on the interface of discontinuity. When the quantity of interest is the jump of the conductivity, we perform a local stability estimate for a parameterized non-monotone family of domains. We give also a quantitative stability result of local optimal solution with respect to a perturbation of the Robin parameter. In order to find an optimal solution, we propose a Kohn–Vogelius-type cost functional over a class of admissible domains subject to two boundary values problems. The analysis of the stability involves the computation of first-order and second-order shape derivative of the proposed cost functional, which is performed rigorously by means of shape-Lagrangian formulation without using the shape sensitivity of the states variables. Copyright © 2016 The Author. Mathematical Methods in the Applied Sciences Published by John Wiley & Sons Ltd.

In the current paper, we consider a stochastic parabolic equation that actually serves as a mathematical model describing the operation of an electrostatic actuated micro-electro-mechanical system. We first present the derivation of the mathematical model. Then after establishing the local well posedeness of the problem, we investigate under which circumstances a finite-time quenching for this stochastic partial differential equation, corresponding to the mechanical phenomenon of touching down, occurs. For that purpose, the Kaplan's eigenfunction method adapted in the context of stochastic partial differential equations is employed. Copyright © 2016 John Wiley & Sons, Ltd.

The paper presents a novel view on the scattering of a flexural wave in a Kirchhoff plate by a semi-infinite discrete system. Blocking and channelling of flexural waves are of special interest. A quasi-periodic two-source Green's function is used in the analysis of the waveguide modes. An additional "effective waveguide" approximation has been constructed. Comparisons are presented for these two methods in addition to an analytical solution for a finite truncated system.

In this paper, we are concerned with the system of the non-isentropic compressible Navier-Stokes equations coupled with the Maxwell equations through the Lorentz force in three space dimensions. The global existence of solutions near constant steady states is established, and the time-decay rates of perturbed solutions are obtained. The proof for existence is due to the classical energy method, and the investigation of large-time behavior is based on the linearized analysis of the non-isentropic Navier-Stokes-Poisson equations and the electromagnetic part for the linearized isentropic Navier-Stokes-Maxwell equations. In the meantime, the time-decay rates obtained by Zhang, Li, and Zhu~[{\it J. Differential Equations, 250(2011), 866-891}] for the linearized non-isentropic Navier-Stokes-Poisson equations are improved.

This paper is concerned with the mathematical analysis of the electromagnetic wave scattering by an unbounded dielectric medium, which is mounted on a perfectly conducting infinite plane. By introducing a transparent boundary condition on a plane surface confining the medium, the scattering problem is modeled as a boundary value problem of Maxwell's equations. Based on a variational formulation, the problem is shown to have a unique weak solution for a wide class of dielectric permittivity and magnetic permeability by using the generalized Lax–Milgram theorem. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we study a multiphasic incompressible fluid model, called the Kazhikhov–Smagulov model, with a particular viscous stress tensor, introduced by Bresch and co-authors, and a specific diffusive interface term introduced for the first time by Korteweg in 1901. We prove that this model is globally well posed in a 3D bounded domain. Copyright © 2016 John Wiley & Sons, Ltd.

This paper is concerned with the control systems of semilinear fractional evolution hemivariational inequalities and their optimal controls in Banach space. Firstly, the existence of mild solutions is obtained and proved mainly by using a well-known fixed point theorem of multivalued maps and the properties of generalized Clarke subdifferential. Then, by applying generally mild conditions of cost functionals, we investigate the existence results of the optimal controls for fractional differential evolution hemivariational inequalities. Finally, an example is given to demonstrate the applicability of the main results. Copyright © 2016 John Wiley & Sons, Ltd.

An optimal boundary control problem in a domain with oscillating boundary has been investigated in this paper. The controls are acting periodically on the oscillating boundary. The controls are applied with suitable scaling parameters. One of the major contribution is the representation of the optimal control using the unfolding operator. We then study the limiting analysis (homogenization) and obtain two limit problems according to the scaling parameters. Another notable observation is that the limit optimal control problem has three controls, namely, a distributed control, a boundary control, and an interface control. Copyright (C) 2016 John Wiley & Sons, Ltd.

In this paper, we study the well-posedness of a coupled Darcy–Oseen resolvent problem, describing the fluid flow between free-fluid domains and porous media separated by a semipermeable membrane. The influence of osmotic effects, induced by the presence of a semipermeable membrane, on the flow velocity is reflected in the transmission conditions on the surface between the free-fluid domain and the porous medium. To prove the existence of a weak solution of the generalized Darcy–Oseen resolvent system, we consider two auxiliary problems: a mixed Navier–Dirichlet problem for the generalized Oseen resolvent system and Robin problem for an elliptic equation related to the general Darcy equations. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we address a simplified version of a problem arising from volcanology. Specifically, as a reduced form of the boundary value problem for the Lame system, we consider a Neumann problem for harmonic functions in the half-space with a cavity C. Zero normal derivative is assumed at the boundary of the half-space; differently, at ∂C, the normal derivative of the function is required to be given by an external datum g, corresponding to a pressure term exerted on the medium at ∂C. Under the assumption that the (pressurized) cavity is small with respect to the distance from the boundary of the half-space, we establish an asymptotic formula for the solution of the problem. Main ingredients are integral equation formulations of the harmonic solution of the Neumann problem and a spectral analysis of the integral operators involved in the problem. In the special case of a datum g, which describes a constant pressure at ∂C, we recover a simplified representation based on a polarization tensor. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we first propose the so-called improved split-step theta methods for non-autonomous stochastic differential equations driven by non-commutative noise. Then, we prove that the improved split-step theta method is convergent with strong order of one for stochastic differential equations with the drift coefficient satisfying a superlinearly growing condition and a one-sided Lipschitz continuous condition. Finally, the obtained results are verified by numerical experiments. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we analyze the behavior of a family of solutions of a nonlinear elliptic equation with nonlinear boundary conditions, when the boundary of the domain presents a highly oscillatory behavior, which is uniformly Lipschitz and nonlinear terms, are concentrated in a region, which neighbors the boundary of domain. We prove that this family of solutions converges to the solutions of a limit problem in H1an elliptic equation with nonlinear boundary conditions which captures the oscillatory behavior of the boundary and whose nonlinear terms are transformed into a flux condition on the boundary. Indeed, we show the upper semicontinuity of this family of solutions.Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we model the growths of populations by means of local fractional calculus. We formulate the local fractional rate equation and the local fractional logistic equation. The exact solutions of local fractional rate equation and local fractional logistic equation with the Mittag-Leffler function defined on Cantor sets are presented. The obtained results illustrate the accuracy and efficiency for modeling the complexity of linear and nonlinear population dynamics (PD). Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, amodel problem that can be used for mathematical modeling and investigation of arc phenomena in electrical contacts is considered. An analytical approach for the solution of a two-phase inverse spherical Stefan problem where along with unknown temperature functions heat flux function has to be determined is presented. The suggested solution method is obtained from a new form of integral error function and its properties that are represented in the form of series whose coefficients have to be determined. Using integral error function and collocation method, the solution of a test problem is obtained in exact form and approximately.

In the present paper we study the vector potential problem in exterior domains of R^3. Our approach is based on the use of weighted spaces in order to describe the behaviour of functions at infinity. As a first step of the investigation, we prove important results on the Laplace equation in exterior domains with Dirichlet or Neumann boundary conditions. As a consequence of the obtained results on the vector potential problem, we establish usefull results on weighted Sobolev inequalities and Helmholtz decompositions of weighted spaces.

In this paper, we prove the existence of mild solutions for the following first-order impulsive semilinear stochastic functional differential inclusions driven by a fractional Brownian motion with infinite delay in the case where the right hand side is convex or nonconvex-valued. The results are obtained by using two fixed point theorems for multivalued mappings. Ministerio de Economía y Competitividad (España) MTM2011-22411 Junta de Andalucía. Consejería de Innovación, Ciencia y Empresa 2010/FQM314 Junta de Andalucía P12-FQM-1492

Y. Wang In this paper, the finite time extinction of solutions to the fast diffusion system ut=div(|∇u|p − 2∇u) + vm, vt=div(|∇v|q − 2∇v) + un is investigated, where 1 0 and is a bounded smooth domain. After establishing the local existence of weak solutions, the authors show that if mn > (p − 1)(q − 1), then any solution vanishes in finite time provided that the initial data are ‘comparable’; if mn = (p − 1)(q − 1) and Ω is suitably small, then the existence of extinction solutions for small initial data is proved by using the De Giorgi iteration process and comparison method. On the other hand, for 1 < p = q < 2 and mn < (p − 1)2, the existence of at least one non-extinction solution for any positive smooth initial data is proved. Copyright © 2015 John Wiley & Sons, Ltd.

The problem of determining the manner in which an incoming acoustic wave is scattered by an elastic body immersed in a fluid is one of the central importance in detecting and identifying submerged objects. The problem is generally referred to as a fluid-structure interaction and is mathematically formulated as a time-dependent transmission problem. In this paper, we consider a typical fluid-structure interaction problem by using a coupling procedure that reduces the problem to a nonlocal initial-boundary problem in the elastic body with a system of integral equations on the interface between the domains occupied by the elastic body and the fluid. We analyze this nonlocal problem by the Lubich approach via the Laplace transform, an essential feature of which is that it works directly on data in the time domain rather than in the transformed domain. Our results may serve as a mathematical foundation for treating time-dependent fluid-structure interaction problems by convolution quadrature coupling of FEM and BEM. Copyright © 2015 John Wiley & Sons, Ltd.

The paper deals with the existence and uniqueness of classical solutions of the homogeneous Neumann problem for a class of parabolic–hyperbolic system of partial differential equations in n dimensions. The problem arises from a model of the diffusion of N species of radioactive isotopes of the same element. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, the stability problem of impulsive functional differential equations with infinite delays is considered. By using Lyapunov functions and the Razumikhin technique, some new theorems on the uniform stability and uniform asymptotic stability are obtained. The obtained results are milder and more general than several recent works. Two examples are given to demonstrate the advantages of the results. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we give positive answer to the open question raised in [E. Zuazua, Exponential decay for the semilinear wave equation with localized damping in unbounded domains. J. Math. Pures Appl., 70 (1991) 513--529] on the exponential decay of solutions for the semilinear plate equation with localized damping., 16 pages

In this paper we study a Large Eddy Simulation (LES) model for the approximation of large scales of the 3D Boussinesq equations. This model is obtained using the approach first described by Stolz and Adams, based on the Van Cittern approximate deconvolution operators, and applied to the filtered Boussinesq equations. Existence and uniqueness of a regular weak solution are provided. Our main objective is to prove that this solution converges towards a solution of the filtered Boussinesq equations, as the deconvolution parameter goes to zero.

In this paper, we are interested in the spatio-temporal dynamics of the transmembrane potential in paced isotropic and anisotropic cardiac tissues. In particular, we observe a specific precursor of cardiac arrhythmias that is the presence of alternans in the action potential duration. The underlying mathematical model consists of a reaction–diffusion system describing the propagation of the electric potential and the nonlinear interaction with ionic gating variables. Either conforming piecewise continuous finite elements or a finite volume-element scheme are employed for the spatial discretization of all fields, whereas operator splitting strategies of first and second order are used for the time integration. We also describe an efficient mechanism to compute pseudo-ECG signals, and we analyze restitution curves and alternans patterns for physiological and pathological cardiac rhythms.

In this paper we study the global existence of small data solutions to the Cauchy problem for the semilinear wave equation with scale-invariant damping. We obtain estimates for the solution and its energy with the same decay rate of the linear problem. We extend our results to a model with polynomial speed of propagation and to a model with an exponential speed of propagation.

This paper is devoted to the study of reverse generalized Bessel matrix polynomials (RGBMPs) within complex analysis. This study is assumed to be a generalization and improvement of the scalar case into the matrix setting. We give a definition of the reverse generalized Bessel matrix polynomials Θn(A; B; z), , for parameter (square) matrices A and B, and provide a second-order matrix differential equations satisfied by these polynomials. Subsequently, a Rodrigues-type formula, a matrix recurrence relationship, and a pseudo-generating function are then developed for RGBMPs. © 2013 The Authors Mathematical Methods in the Applied Sciences Published by John Wiley & Sons, Ltd.

This paper analyzes the existence and the uniqueness problem for an n-dimensional nonlinear inverse reaction-diffusion problem with a nonlinear source. A transformation is used to obtain a new inverse coefficient problem. Then, a parabolic differential operator L is defined to establish the relation between the solution of L=0 and the new inverse problem. Following this, it is shown that the inverse problem has at least one solution in the class of admissible coefficients. Furthermore, it is proved that this solution is the unique solution of the undertaken inverse problem. A numerical example is given to illustrate ill-posedness of the inverse problem. Copyright (c) 2013 John Wiley & Sons, Ltd.

In this paper, we consider a nonhomogeneous space-time fractional telegraph equation defined in a bounded space domain, which is obtained from the standard telegraph equation by replacing the first-order or second-order time derivative by the Caputo fractional derivative Dtα, α > 0 and the Laplacian operator by the fractional Laplacian ( − Δ)β ∕ 2, β ∈ (0,2]. We discuss and derive the analytical solutions under nonhomogeneous Dirichlet and Neumann boundary conditions by using the method of separation of variables. The obtained solutions are expressed through multivariate Mittag-Leffler type functions. Special cases of solutions are also discussed. Copyright © 2013 John Wiley & Sons, Ltd.

Due to copyright restrictions, the access to the full text of this article is only available via subscription. In the present paper, the two-step difference scheme for the Cauchy problem for the stochastic hyperbolic equation is presented. The convergence estimate for the solution of the difference scheme is established. In applications, the convergence estimates for the solution of difference schemes for the numerical solution of four problems for hyperbolic equations are obtained. The theoretical statements for the solution of this difference scheme are supported by the results of the numerical experiment.