Cauchy problem in the non-classical treatment for one pseudoparabolic equation

TL;DR

This paper investigates the Cauchy problem for a fifth-order pseudoparabolic equation with non-classical conditions, establishing equivalence with classic conditions in Sobolev anisotropic spaces, relevant for fluid and moisture transfer modeling.

Contribution

It introduces a non-classical approach to the Cauchy problem for pseudoparabolic equations with discontinuous coefficients, proving their equivalence to classical conditions in specific function spaces.

Findings

Non-classical conditions do not require agreement conditions.

Equivalence of non-classical and classical conditions in Sobolev anisotropic spaces.

Applicability to modeling fluid and moisture transfer processes.

Abstract

In the paper, we consider the Cauchy problem for a fifth order pseudoparabolic equation that appears in studying the issues of fluid filtration in fissured media, the moisture transfer in soils and etc. The Cauchy problem with non-classic conditions not requiring the agreement conditions are studied for a discontinuous coefficient pseudoparabolic equation. The equivalence of these conditions with the Cauchy classic condition is substantiated in the case when the solution of the stated problem is sought in S.L.Sobolev anisotropic space.