Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 2, Pages 181-195
doi:10.1155/S1048953300000198

On a third order parabolic equation with a nonlocal boundary condition

Abdelfatah Bouziani

Centre Universitaire d'Oum El Bouaghi, Département de Mathématiques, B.P. 565, Oum E1 Bouaghi 04000, Algeria

Received 1 January 1997; Revised 1 December 1997

Copyright © 2000 Hindawi Publishing Corporation. 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

In this paper we demonstrate the existence, uniqueness and continuous dependence of a strong solution upon the data, for a mixed problem which combine classical boundary conditions and an integral condition, such as the total mass, flux or energy, for a third order parabolic equation. We present a functional analysis method based on an a priori estimate and on the density of the range of the operator generated by the studied problem.