Cauchy Problem in the Non-Classical Treatment for One Pseudoparabolic Equation

Ilgar G Mamedov

doi:10.13189/ujcmj.2014.020101

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 ( ) ( ) 3,2 p WG .

Highlights

In the present paper, here consider Cauchy problem for one higher order differential equation with discontinuous coefficients
Many processes arising in the theory of fluid filtration in cracked media are described by discontinuous coefficient pseudoparabolic equations
In the paper a non-classical type Cauchy problem is substantiated for a pseudoparabolic equation with non-smooth coefficients and with a fifth order dominating derivative

Summary

Introduction

Here consider Cauchy problem for one higher order differential equation with discontinuous coefficients The coefficients in this pseudoparabolic equation are not necessarily differentiable; there does not exist a formally ad joint differential equation making a certain sense. The theme of the present paper, devoted to the investigation Cauchy problem for one differential equations of pseudoparabolic type, according to the above-stated is very actual for the solution of theoretical and practical problems. From this point of view, the paper is devoted to the actual problems of partial differential equations and computational mathematics

Problem Statement

Result

Discussion and Conclusions