On Nonlinear Nonlocal Systems of Reaction Diffusion Equations - B. Ahmad; M. S. Alhothuali; H. H. Alsulami; M. Kirane; S. Timoshin (Abstract and Applied Analysis)
The reaction diffusion system with anomalous diffusion and a balance law ut+-Δα/2u=-fu,v,   vt+-∆β/2v=fu,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.