On Nonlinear Nonlocal Systems of Reaction Diffusion Equations

The reaction diffusion system with anomalous diffusion and a balance law u t + - Δ α / 2 u = - f u , v , v t + - ∆ β / 2 v = f u , v , 0 < α , β < 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 < α ≤ β ≤ 2 ; (ii) no growth condition is imposed on the reaction term f when 0 < β ≤ α ≤ 2 .