Related papers: Methods for solution of boundary value problems in…
We provide a new approach to obtain solutions of certain evolution equations set in a Banach space and equipped with nonlocal boundary conditions. From this approach we derive a family of numerical schemes for the approximation of the…
We consider a boundary value problem for the conductivity equation in a bounded domain containing an inclusion which is nearly touching to the domain's boundary. We assume that the domain and the inclusion are disks with conductivity jump…
By means of topological methods, we provide new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for systems of perturbed Hammerstein integral equations. In order to illustrate our theoretical…
In this article we study a class of generalised linear systems of difference equations with given boundary conditions and assume that the boundary value problem is non-consistent, i.e. it has infinite many or no solutions. We take into…
We study the initial-boundary value problem for a class of diffusion equations with nonmonotone diffusion flux functions, including forward-backward parabolic equations and the gradient flows of nonconvex energy functionals, under the…
In this paper we study the solvability of different boundary value problems for the two dimensional steady incompressible Euler equation. Two main methods are currently available to study those problems, namely the Grad-Shafranov method and…
We develop a new semi-analytical method for solving multilayer diffusion problems with time-varying external boundary conditions and general internal boundary conditions at the interfaces between adjacent layers. The convergence rate of the…
Fractional boundary value problems are often used to model complex systems and processes characterized by memory effects and anomalous diffusion. In this paper, we consider fractional boundary value problems involving the Riesz-Caputo…
For one class of boundary value problem depending on small parameter for which numerical methods for their solution are actually inapplicable, procedure of limiting problem acquisition which is much easier and which solution as much as…
In this paper, we obtained the sufficient conditions for the existence of solutions to the discrete boundary value problems of fractional difference equation depending on parameters. We use Krasnoselskii fixed point theorem to establish the…
We consider existence of periodic boundary value problems of nonlinear second order ordinary differential equations. Under certain half Lipschitzian type conditions several existence results are obtained. As applications positive periodic…
The purpose of this article is to study extrapolation of solvability for boundary value problems of elliptic systems in divergence form on the upper half-space assuming De Giorgi type conditions. We develop a method allowing to treat each…
Given only a collection of points sampled from a Riemannian manifold embedded in a Euclidean space, in this paper we propose a new method to solve elliptic partial differential equations (PDEs) supplemented with boundary conditions. Notice…
In this paper we propose a Local Orthogonal Decomposition method (LOD) for elliptic partial differential equations with inhomogeneous Dirichlet- and Neumann boundary conditions. For this purpose, we present new boundary correctors which…
In this paper, we suggest a technique to avoid order reduction in time when integrating reaction-diffusion boundary value problems under non-homogeneous boundary conditions with exponential splitting methods. More precisely, we consider…
The creation and justification of the methods for minimax estimation of parameters of the external boundary value problems for the Helmholtz equation in unbounded domains are considered. When observations are distributed in subdomains, the…
We study the diffusion (or heat) equation on a finite 1-dimensional spatial domain, but we replace one of the boundary conditions with a "nonlocal condition", through which we specify a weighted average of the solution over the spatial…
This article is concerned with the existence and uniqueness of solutions to some fractional order boundary value problems. Our results are based on some fixed point theorems. For the applicability of our results, we provide an example.
Convection-diffusion problems arise in the modelling of many physical processes. Their typical solutions exhibit boundary and/or interior layers. Despite the linear nature of the differential operator, these problems pose still-unanswered…
We derive an explicit representation of the fundamental solution to the heat equation in a half-space of ${\mathbb R}^N$ with a diffusive dynamical boundary condition, and establish sharp pointwise upper and lower bounds. We also…