Nonexistence of positive solutions to a quasilinear elliptic system and blow-up estimates for a quasilinear reaction–diffusion system

The prior estimate and decay property of positive solutions are derived for a system of quasilinear elliptic differential equations first. Then, the nonexistence result for radially nonincreasing positive solutions of the system is implied. By using this nonexistence result, blow-up estimates for a class of quasilinear reaction–diffusion systems (non-Newtonian filtration systems) are established to extend the result for semilinear reaction–diffusion systems (Fujita type).