Abstract and Applied Analysis
Volume 2004 (2004), Issue 9, Pages 793-813
On a class of nonlinear reaction-diffusion systems with nonlocal boundary conditions
Department of Mathematics, The Larbi Ben M'hidi University Centre, P. O. Box 565, Oum El Bouaghi 04000, Algeria
Received 30 July 2003
Copyright © 2004 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.
We prove the existence, uniqueness, and continuous dependence of a generalized solution of a nonlinear reaction-diffusion system with only integral terms in the boundaries. We first solve a particular case of the problem by using the energy-integral method. Next, via an iteration procedure, we derive the obtained results to study the solvability of the stated problem.