On nonlinear nonlocal systems of reaction diffusion equations

Abstract

The reaction diffusion system with anomalous diffusion and a balance law u t+ (-Δ)α/2 u = - f (u, v), vt + (-Δ)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. © 2014 B. Ahmad et al.