On One Solution of a Periodic Boundary-Value Problem for a Third-Order Pseudoparabolic Equation

Abstract

This article is devoted to the study of the solvability of a periodic boundary-value problem for a third-order pseudoparabolic equation with a mixed derivative. Nonlocal problems for pseudoparabolic equations have been investigated by many authors. Of particular interest in the study of these problems is caused in connection with their applied values. Such problems include highly porous media with a complex topology, and first of all, soil and ground. To solve this problem, new functions are introduced and the boundary-value problem for a third-order pseudoparabolic equation is reduced to a periodic boundary-value problem for a system of hyperbolic equations with a second-order mixed derivative. Based on the equivalence of the boundary-value problem for a system of hyperbolic equations and the periodic boundary-value problem for a family of systems of ordinary differential equations, two-parameter families of algorithms for finding an approximate solution are constructed and the conditions for unambiguous solvability of the problem under study are established.