Asymptotic bounds for solutions of a periodic reaction diffusion system

The purpose of this paper is to investigate the asymptotic behavior of nonnegative solutions of a periodic reaction diffusion system. By De Giorgi iteration technique, we obtain the a priori upper bound of nonnegative periodic solutions of the considered periodic system. We then establish the existence of the maximum periodic solution and asymptotic bounds of nonnegative solutions of the initial boundary value problem.