Goursat problem in the non-classical treatment for a sixth order pseudoparabolic equation

TL;DR

This paper investigates a Goursat problem with non-classical boundary conditions for a sixth-order pseudoparabolic equation, demonstrating the problem's well-posedness in Sobolev anisotropic spaces without the need for agreement conditions.

Contribution

It establishes the solvability of the Goursat problem with non-classical boundary conditions for a sixth-order pseudoparabolic equation in Sobolev anisotropic spaces, removing the necessity of agreement conditions.

Findings

The Goursat problem is well-posed in Sobolev anisotropic spaces.

Non-classical boundary conditions do not require agreement conditions.

The classical boundary condition case is substantiated within this framework.

Abstract

In the paper the Goursat problem with non classical boundary conditions not requiring the agreement conditions is considered for a sixth order pseudoparabolic equation with the classical boundary condition is substantiated in the case if the solution of the stated problem is sought in S.L.Sobolev anisotropic space.