The Existence and Uniqueness of a New Boundary Value Problem (Type of Problem “E”) for Linear System Equations of the Mixed Hyperbolic-Elliptic Type in the Multivariate Dimension with the Changing Time Direction

Mahammad A Nurmammadov

doi:10.1155/2015/703652

Abstract

The existence and uniqueness of the boundary value problem for linear systems equations of the mixed hyperbolic-elliptic type in the multivariate domain with the changing time direction are studied. Applying methods of functional analysis, “ε-regularizing” continuation by the parameter and by means of prior estimates, the existence and uniqueness of generalized and regular solutions of a boundary problem are established in a weighted Sobolev space.

Highlights

Up to the present, various generalizations of mixed and composite type of equations have been investigated by many authors
Interest of investigations of nonclassical equations arises in applications in the field of hydrogas dynamics, modeling of physical processes
Nonclassical model is defined as the model of mathematical physics, which is represented in the form of the equation or systems of partial differential equations that does not fit into one of the classical types: elliptic, parabolic, or hyperbolic

Summary

Introduction

Various generalizations of mixed and composite type of equations have been investigated by many authors. The existence and uniqueness of the boundary value problem for linear systems equations of the mixed hyperbolic-elliptic type in the multivariate domain with the changing time direction are studied. One says that u(x, t) and υ(x, t) are regular solution of problem ((1)–(4)), if the functions u(x, t), υ(x, t) ∈ H2,L(D) satisfy equation of (1) almost everywhere in domain D.

Results

Conclusion