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Abstract and Applied Analysis
Volume 2014, Article ID 804784, 6 pages
http://dx.doi.org/10.1155/2014/804784
Research Article

On Nonlinear Nonlocal Systems of Reaction Diffusion Equations

1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Laboratoire de Mathématiques, Images et Applications, Pôle Sciences et Technologies, Université de La Rochelle, Avenue M. Crepeau, 17031 La Rochelle, France
3Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK

Received 17 April 2014; Revised 9 June 2014; Accepted 9 June 2014; Published 23 June 2014

Academic Editor: Juan J. Nieto

Copyright © 2014 B. Ahmad et al. 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

The reaction diffusion system with anomalous diffusion and a balance law ,   , , , is con sidered. The existence of global solutions is proved in two situations: (i) a polynomial growth condition is imposed on the reaction term when ; (ii) no growth condition is imposed on the reaction term when .