Blow up of nonautonomous fractional reaction-diffusion systems

Abstract

. We provide a suf fi cient condition for fi nite time blow up of the positive mild solution to the nonautonomous Cauchy problem of a reaction-diffusion system with distinct fractional diffusions. The proof is based on the reduction to an ordinary differential system by means of a comparison between the transition densities of the semigroups generated by the different fractional Laplacians. Moreover, we prove that this condition is also a suf fi cient condition for the blow up of a related nonautonomous fractional diffusion-convection-reaction system.