相关论文: Integrable initial boundary value problems
A new method is introduced for studying boundary value problems for a class of linear PDEs with {\it variable} coefficients. This method is based on ideas recently introduced by the author for the study of boundary value problems for PDEs…
An initial-boundary value problem with homogeneous Dirichlet boundary conditions for three-dimensional Zakharov-Kuznetsov equation is considered. Results on global existence, uniqueness and large-time decay of weak solutions in certain…
We consider an inhomogeneous initial-boundary value problem for a Petrovskii parabolic system of second order PDEs. We prove that this problem induces isomorphisms between appropriate anisotropic generalized Sobolev spaces. The regularity…
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…
The paper considers existence of spatially regular solutions for a class of linear Boltzmann transport equations. The related transport problem is an (initial) inflow boundary value problem. This problem is characteristic with variable…
Solutions of boundary value problems for a diffusion equation of fractional and variable order in differential and difference settings are studied. It is shown that the method of energy inequalities is applicable to obtaining a priori…
In this paper, we explore the initial-boundary value (IBV) problem for an integrable spin-1 Gross-Pitaevskii system with a 4x4 Lax pair on the finite interval by extending the Fokas unified transform approach. The solution of this system…
The aim of the paper is to develop a general theory of solvability of linear inhomogeneous boundary-value problems for systems of ordinary differential equations of arbitrary order in Sobolev spaces. Boundary conditions are allowed to be…
Initial boundary value problem on a half-line for the Modified KdV equation is considered with the boundary conditions equal to zero at the origin and initial condition chosen arbitrary decreasing rapidly enough and this problem is plunged…
The Direct and the Inverse Scattering Problems for the heat operator with a potential being a perturbation of an arbitrary $N$ soliton potential are formulated. We introduce Jost solutions and spectral data and present their properties.…
In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP) for the following second-order differential equation \begin{equation*} \begin{gathered} {u^{\prime \prime }}(t)+\lambda…
We consider boundary value problems of the first and third kind for the diffusionwave equation. By using the method of energy inequalities, we find a priori estimates for the solutions of these boundary value problems.
In this paper, we apply Fokas unified method to study initial-boundary value problems for the two-component Gerdjikov-Ivanov equation formulated on the finite interval with $3 \times 3$ Lax pairs. The solution can be expressed in terms of…
We study multidimensional difference equations with a continual variable in the Sobolev--Slobodetskii spaces. Using ideas and methods of the theory of boundary value problems for elliptic pseudo differential equations we suggest to consider…
The flow of a gas through porous medium is considered in the case of pressure dependent permeability. Approximate self-similar solutions of the boundary-value problems are found.
Initial-boundary value problems in a half-strip with different types of boundary conditions for two-dimensional Zakharov-Kuznetsov equation are considered. Results on global well-posedness in classes of regular solutions in the cases of…
We study boundary integral formulations for an interior/exterior initial boundary value problem arising from the thermo-elasto-dynamic equations in a homogeneous and isotropic domain. The time dependence is handled, based on Lubich's…
We will establish uniqueness of solutions to boundary value problems involving the nabla Caputo fractional difference under two-point boundary conditions and give an explicit expression for the Green's functions for these problems. Using…
The paper considers the system of pressureless gas dynamics in one space dimension. The question of solvability of the initial-boundary value problem is addressed. Using the method of generalized potentials and characteristic triangles,…
The paper considers a boundary value problem for the high-order Lavrent'ev-Bitsadze equation. Necessary and sufficient conditions for the uniqueness of the solution are found. When substantiating the existence, the problem of "small…