Abstract
The reaction diffusion system with anomalous diffusion and a balance law u(f) +(-Delta)(alpha/2)u = -f (u, V), V-t +(-Delta)(beta/2) V = f (mu, V), 0 < alpha, beta < 2, is con sidered. The existence of global solutions is proved in two situations: (i) a polynomial growth condition is imposed on the reaction term f when 0 < alpha <= beta <= 2; (ii) no growth condition is imposed on the reaction term f when 0 < beta <= alpha <= 2.