Journal of Applied Mathematics and Stochastic Analysis
Volume 2009 (2009), Article ID 975601, 13 pages
doi:10.1155/2009/975601
Research Article

A Boundary Value Problem with Multivariables Integral Type Condition for Parabolic Equations

A. L. Marhoune1 and F. Lakhal2

1Laboratory Equations Différentielles, Departement of Mathematics, University Mentouri Constantine, Constantine 25017, Algeria
2Department of Mathematics, Science University of 08 Mai 45, P.O. Box 401, Guelma 24000, Algeria

Received 27 January 2009; Revised 14 May 2009; Accepted 13 October 2009

Academic Editor: Sergiu Aizicovici

Copyright © 2009 A. L. Marhoune and F. Lakhal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study a boundary value problem with multivariables integral type condition for a class of parabolic equations. We prove the existence, uniqueness, and continuous dependence of the solution upon the data in the functional wieghted Sobolev spaces. Results are obtained by using a functional analysis method based on two-sided a priori estimates and on the density of the range of the linear operator generated by the considered problem.