On a problem with conditions on all boundary for a pseudoparabolic equation

TL;DR

This paper investigates a sixth-order pseudoparabolic boundary value problem with non-classical boundary conditions, establishing their equivalence to classical conditions within Sobolev spaces, thus broadening understanding of boundary condition formulations.

Contribution

It demonstrates the equivalence of non-classical boundary conditions with classical ones for a sixth-order pseudoparabolic equation in Sobolev spaces, without requiring agreement conditions.

Findings

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

The problem does not require agreement conditions on the boundary.

The equivalence broadens the applicability of boundary conditions in pseudoparabolic equations.

Abstract

A problem with non-classical conditions on all the boundary not requiring agreement conditions is considered for a sixth order pseudoparapolic equation. The equivalence of these conditions with the classic boundary condition is substantiated in the case if the solution of the stated problem is sought in S.L.Sobolev isotropic space.