On Nonlinear Nonlocal Systems of Reaction Diffusion Equations

Abstract

The reaction diffusion system with anomalous diffusion and a balance law $u_t+{\left(-\mathrm{\Delta }\right)}^{\alpha /2}u=-f\left(u,v\right)$, $\hspace{0.17em}{v}_t+{\left(-∆\right)}^{\beta /2}v=f\left(u,v\right)$, , , 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 ; (ii) no growth condition is imposed on the reaction term $f$ when .