Solvability of a semi-periodic boundary value problem for a third order differential equation with mixed derivative

Abstract

This article is devoted to the study of the solvability of a semi-periodic boundary value problem for an evolution equation of the pseudoparabolic type. Nonlocal problems for high order partial differential equations have been investigated by many authors [1–4]. A certain interest in the study of these problems is caused in connection with their applied values. These problems include highly porous media with a complex topology, and first of all, soil and ground. Such equations can also describe long waves in dispersed systems. To solve this problem, new functions are introduced in the work and the method of a parameterizations applied [5]. Then the boundary value problem for a third order differential equation is reduced to a periodic boundary value problem for a family of systems of ordinary differential equations [6–18]. New constructive algorithms for finding an approximate solution are proposed and in terms of the initial data, coefficient-like signs of the unique solvability of the problem under study are obtained.