Contact-boundary value problem in the non-classical treatment for one pseudoparabolic equation

TL;DR

This paper investigates a contact-boundary value problem for a pseudoparabolic equation with non-classical conditions, establishing their equivalence in Sobolev spaces, thus broadening the understanding of boundary conditions in such equations.

Contribution

It introduces and analyzes non-classical boundary conditions for pseudoparabolic equations, proving their equivalence without requiring agreement conditions in Sobolev spaces.

Findings

Non-classical boundary conditions are equivalent to classical ones in Sobolev spaces.

The approach removes the need for agreement conditions in boundary value problems.

The study extends the theoretical framework for pseudoparabolic equations.

Abstract

In the paper, the contact - boundary value problem with non-classical conditions not requiring agreement conditions is considered for a pseudoparabolic equation. The equivalence of these conditions is substantiated in the case if the solution of the solution of the stated problem is sought in S.L.Sobolev isotropic space.