MIXED PROBLEM WITH AN INTEGRAL SPACE VARIABLE CONDITION FOR A THIRD ORDER PARABOLIC EQUATION OF MIXED TYPE

A. L. Marhoune (Algeria) and A. Hameida (Algeria)

Received June 26, 2007

Abstract

In this paper we study a mixed problem with an integral space variable condition for a parabolic equation of mixed type. The existence and uniqueness of the solution in a functional weighted Sobolev space are proved. The proof is based on two sided a priori estimates and the density of the range of the operator generated by the considered problem.

Keywords and phrases: parabolic equation of mixed type, three-point boundary condition, integral space variable condition, energy inequalities, weighted Sobolev space.