相关论文: Initial-boundary value problems for linear PDEs: t…
In this paper, we deal with analysis of the initial-boundary value problems for the semilinear time-fractional diffusion equations, while the case of the linear equations was considered in the first part of the present work. These equations…
Initial-boundary value problems for 1-dimensional `completely integrable' equations can be solved via an extension of the inverse scattering method, which is due to Fokas and his collaborators. A crucial feature of this method is that it…
Boundary integral equations are an efficient and accurate tool for the numerical solution of elliptic boundary value problems. The solution is expressed as a layer potential; however, the error in its evaluation grows large near the…
We show that infinitely differentiable solutions to parabolic and hyperbolic equations, whose right-hand sides are analytical in time, are also analytical in time at each fixed point of the space. These solutions are given in the form of…
Nonlinear control-affine systems described by ordinary differential equations with bounded measurable input functions are considered. The solvability of general boundary value problems for these systems is formulated in the sense of…
This work investigates the application of the Newton's method for the numerical solution of a nonlinear boundary value problem formulated through an ordinary differential equation (ODE). Nonlinear ODEs arise in various mathematical modeling…
An initial-boundary value problem for a time-fractional subdiffusion equation with the Riemann-Liouville derivatives on N-dimensional torus is considered. The uniqueness and existence of the classical solution of the posed problem are…
Initial-boundary value problems for 1-dimensional `completely integrable' equations can be solved via an extension of the inverse scattering method, which is due to Fokas and his collaborators. A crucial feature of this method is that it…
Motivated by applications in economics and finance, in particular to the modeling of limit order books, we study a class of stochastic second-order PDEs with non-linear Stefan-type boundary interaction. To solve the equation we transform…
This article studies a priori error analysis for linear parabolic interface problems with measure data in time in a bounded convex polygonal domain in $\mathbb{R}^2$. We have used the standard continuous fitted finite element discretization…
In this paper, we investigate the existence of nontrivial weak solutions for the Prandtl-Batchelor type free boundary value elliptic problem driven by a power nonlinearity. The algebraic topology approach will be used to establish the…
In many numerical implementations of the Cauchy formulation of Einstein's field equations one encounters artificial boundaries which raises the issue of specifying boundary conditions. Such conditions have to be chosen carefully. In…
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 initial-boundary value problem for the two-dimensional regular four-velocity discrete Boltzmann system is analyzed in a rectangle. The existence and uniqueness of a classical global positive solution, bounded with its first partial…
Two-point boundary value problems for a discrete Ermakov-Painlev\'e II equation are analysed by means of topological methods. In addition, an alternative variational approach is detailed. Existence of solutions is established for…
The paper is concerned with the interconnection of the boundary behaviour of the solutions of the exterior Dirichlet and Neumann problems of harmonic analysis for the three-dimensional unit ball with the corresponding behaviour of the…
The main objective of this paper is analysis of the initial-boundary value problems for the linear time-fractional diffusion equations with a uniformly elliptic spatial differential operator of the second order and the Caputo type…
In this article, we focus on a doubly nonlinear nonlocal parabolic initial boundary value problem driven by the fractional $p$-Laplacian equipped with homogeneous Dirichlet boundary conditions on a domain in $\mathbb{R}^{d}$ and composed…
We derive new boundary conditions and implementation procedures for nonlinear initial boundary value problems (IBVPs) with non-zero boundary data that lead to bounded solutions. The new boundary procedure is applied to nonlinear IBVPs in…
We investigate an initial-(periodic-)boundary value problem for a continuum equation, which is a model for motion of grain boundaries based on the underlying microscopic mechanisms of line defects (disconnections) and integrated the effects…