Related papers: Analytic regularity for a singularly perturbed rea…
Boundary value problems for linear stationary dispersive equations of order $2l+1$, $l\in \mathbb{N}$ have been considered on finite intervals $(0,L)$. The existence and uniqueness of regular solutions have been established for general…
The work is devoted to the construction of the asymptotic behavior of the solution of a singularly perturbed system of equations of parabolic type, in the case when the limit equation has a regular singularity as the small parameter tends…
A finite difference method is constructed for a singularly perturbed convection diffusion problem posed on an annulus. The method involves combining polar coordinates, an upwind finite difference operator and a piecewise-uniform Shishkin…
This paper is concerned with the existence and the regularity of global solutions to the linear wave equation associated with two-point type boundary conditions. We also investigate the decay properties of the global solutions to this…
In this article, we present a numerical approach to ensure the preservation of physical bounds on the solutions to linear and nonlinear hyperbolic convection-reaction problems at the discrete level. We provide a rigorous framework for error…
We consider variational inequality solutions with prescribed gradient constraints for first order linear boundary value problems. For operators with coefficients only in $L^2$, we show the existence and uniqueness of the solution by using a…
This article investigates the non-stationary reaction-diffusion-advection equation, emphasizing solutions with internal layers and the associated inverse problems. We examine a nonlinear singularly perturbed partial differential equation…
In this note we propose the exact artificial boundary conditions formula to the fractional reaction-subdiffusion equation on an unbounded domain. With the application of Laplace transformation, the exact artificial boundary conditions…
This work is motivated by the frequent occurrence of boundary value problems with various boundary conditions in the modeling of some problems in engineering and physical science. Here we propose a new technique to force the positive…
We aim at the development and analysis of the numerical schemes for approximately solving the backward diffusion-wave problem, which involves a fractional derivative in time with order $\alpha\in(1,2)$. From terminal observations at two…
We derive the fully time-dependent solution to a run-and-tumble model for a particle which has tumbling restricted to the boundaries of a one-dimensional interval. This is achieved through a field-theoretic perturbative framework by…
We investigate Turing instability and pattern formation in two-dimensional domains for two reaction-diffusion models, obtained as diffusive limits of kinetic equations for mixtures of monatomic and polyatomic gases. The first model is of…
Boundary value problem for complete second order elliptic equation is considered in Banach space. The equation and boundary conditions involve a small and spectral parameter. The uniform L_{p}-regularity properties with respect to space…
An initial-boundary value problem for the time-fractional diffusion equation is discretized in space using continuous piecewise-linear finite elements on a polygonal domain with a re-entrant corner. Known error bounds for the case of a…
The existence of numerical solutions to a fourth order singular boundary value problem arising in the theory of epitaxial growth is studied. An iterative numerical method is applied on a second order nonlinear singular boundary value…
We consider a wide class of fully nonlinear integro-differential equations that degenerate when the gradient of the solution vanishes. By using compactness and perturbation arguments, we give a complete characterization of the regularity of…
This work unifies pseudo-time and inexact regularization techniques for nonmonotone classes of partial differential equations, into a regularized pseudo-time framework. Convergence of the residual at the predicted rate is investigated…
We present a numerical approximation method for linear diffusion-reaction problems with possibly discontinuous Dirichlet boundary conditions. The solution of such problems can be represented as a linear combination of explicitly known…
The goal of this work is to compute a boundary control of reaction-diffusion partial differential equation. The boundary control is subject to a constant delay, whereas the equation may be unstable without any control. For this system…
An initial-boundary value problem for a subdiffusion equation with an elliptic operator $A(D)$ in $\mathbb{R}^N$ is considered. The existence and uniqueness theorems for a solution of this problem are proved by the Fourier method.…