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

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.