Related papers: Solvability of the boundary value problem for some…
In the paper the conditions are obtained providing existence and uniqueness of the regular solution of the boundary problem for class of the second order homogeneous operator-differential equation with singular coefficients. High term of…
We consider the Fredholm one-dimensional boundary-value problems in Sobolev spaces.We have obtained several important results about the indixes of functional operators, the criterion of their correct well-posedness, the criterion of the…
Numerical solutions of differential equations are usually not smooth functions. However, they should resemble the smoothness of the corresponding real solutions in one way or another. In two of our recent papers, a kind of spacial…
The article is devoted to the solvability of a system of integro-differential equations in the case of the difference of the standard Laplacian and the bi-Laplacian in the diffusion terms. The proof of the existence of solutions is based on…
We study properties of pseudodifferential operators which arise in their use in boundary value problems. Smooth domains as well as intersections of smooth domains are considered.
An initial-boundary value problem for a generalized KdV equation posed on a half-line is considered. Existence and uniqueness of global regular solutions for arbitrary smooth initial data are established.
We focus on the initial boundary value problem for a general scalar balance law in one space dimension. Under rather general assumptions on the flux and source functions, we prove the well-posedness of this problem and the stability of its…
We prove the existence of solutions for some integro-differential systems containing equations with and without the drift terms in the H^2 spaces by virtue of the fixed point technique when the elliptic equations contain second order…
This article provides a general iterative approximation to partial differential equations, and thus establish existence of smooth solution. The heart of the method is to contract (or expand) the boundary conditions uniformly in the domain,…
Some approach to the solution of boundary value problems for finding functions, which are analytical in a wedge, is proposed. If the ratio of the angle at the wedge vertex to a number \pi is rational, then the boundary value problem is…
The linear boundary value problem under consideration describes time-harmonic motion of water in a horizontal three-dimensional layer of constant depth in the presence of an obstacle adjacent to the upper side of the layer (floating body).…
By employing a novel generalization of the inverse scattering transform method known as the unified transform or Fokas method, it can be shown that the solution of certain physically significant boundary value problems for the elliptic…
A numerical scheme is presented for the solution of Fredholm second-kind boundary integral equations with right-hand sides that are singular at a finite set of boundary points. The boundaries themselves may be non-smooth. The scheme, which…
We prove existence of positive solutions to a boundary value problem depending on discrete fractional operators. Then, corresponding discrete fractional Lyapunov-type inequalities are obtained.
Here a mixed problem for a nonlinear hyperbolic equation with Neumann boundary value condition is investigated, and a priori estimations for the possible solutions of the considered problem are obtained. These results demonstrate that any…
In a refined Sobolev scale, we investigate an elliptic boundary-value problem with additional unknown functions in boundary conditions for which the maximum of orders of boundary operators is grater than or equal to the order of the…
We study elliptic and parabolic boundary value problems in spaces of mixed scales with mixed smoothness on the half space. The aim is to solve boundary value problems with boundary data of negative regularity and to describe the…
In this paper, we study the separability and spectral properties of singular degenerate elliptic equations in vector valued spaces. We prove that a realization operator by this equation with some boundary conditions is separable and…
Investigating the stability of nonlinear waves often leads to linear or nonlinear eigenvalue problems for differential operators on unbounded domains. In this paper we propose to detect and approximate the point spectra of such operators…
A meromorphic solution of a complex linear differential equation (with meromorphic coefficients) for which the value zero is the only possible finite deficient/deviated value is called a standard solution. Conditions for the existence and…