Dirichlet problem in the non-classical treatment for one pseudoparabolic equation of fourth order

TL;DR

This paper investigates a Dirichlet problem for a fourth-order pseudoparabolic equation with non-classical boundary conditions, establishing their equivalence to classical conditions within Sobolev spaces, thus broadening solution frameworks.

Contribution

It introduces a non-classical boundary condition approach for the fourth-order pseudoparabolic equation and proves their equivalence to classical conditions in Sobolev spaces.

Findings

Non-classical conditions do not require agreement conditions

Equivalence of non-classical and classical boundary conditions established

Solution framework extended to Sobolev isotropic spaces

Abstract

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