Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 2, Pages 181-195
On a third order parabolic equation with a nonlocal boundary condition
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 Abdelfatah Bouziani. 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.
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.