Final-boundary value problem in the non-classical treatment for a sixth order pseudoparabolic equation

TL;DR

This paper investigates a final-boundary value problem for a sixth-order pseudoparabolic equation using non-classical boundary conditions, establishing their equivalence to classical conditions within Sobolev anisotropic spaces.

Contribution

It introduces non-classical boundary conditions for the sixth-order pseudoparabolic equation and proves their equivalence to classical conditions in Sobolev anisotropic spaces.

Findings

Non-classical boundary conditions are equivalent to classical ones.

The problem is well-posed in Sobolev anisotropic spaces.

The approach broadens the understanding of boundary conditions for high-order pseudoparabolic equations.

Abstract

For this equation we consider a final-boundary value problem with non-classical conditions not requiring agreement conditions. 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 anisotropic space.