International Journal of Pure and Applied Mathematics Volume 102 No. 2 2015, 169-186 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: http://dx.doi.org/10.12732/ijpam.v102i2.1 P A ijpam.eu EXISTENCE OF GLOBAL SOLUTIONS FOR SYSTEMS OF REACTION-DIFFUSION WITH COMPACT RESULT Abdelkader Moumeni 1 , Nabila Barrouk 2 § 1,2 Laboratoire de Math´ ematiques Dynamique et Mod´ elisation Universit´ e Badji Mokhtar-Annaba B.P. 12 Annaba 23000, ALG ´ ERIE 2 Department of Mathematics and Informatics Faculty of Sciences University of Souk Ahras 41000, Souk Ahras, ALGERIA Abstract: The aim of this paper is to study the global existence in time of solutions for some class of reaction-diffusion systems. Our techniques of proof is based on compact semigroup methods and some L 1 estimates. Our goal is to show, under suitable assumptions, that the proposed model have a global solution for a large class of the functions f and g. AMS Subject Classification: 35K57, 35K40, 35K55 Key Words: global solution, semi-groups, local solution, reaction-diffusion systems 1. Introduction Recently, a class of systems of partial differential equations of the parabolic type, called system of reaction-diffusion, it received considerable interest by the Received: December 18, 2014 c  2015 Academic Publications, Ltd. url: www.acadpubl.eu § Correspondence author