Blow-up Estimates for a Semilinear Reaction-diffusion System

Abstract

The prior estimate and decay property of positive solutions are derived for a system of semilinear elliptic differential equations first. Hence, the result of nonexistence for differential equation system of radially nonincreasing positive solutions is implied. By using this nonexistence result, we establish blow-up estimates for a class semilinear reaction-diffusion systems(Newtonian filtration systems), which extends the result of semilinear reaction-diffusion(Fujita type) systems.