Blow-Up Estimates for a Non-Newtonian Filtration System

The prior estimate and decay property of positive solutions are derived for a system of quasi_linear elliptic differential equations first. Hence, the result of non_existence for differential equation system of radially nonincreasing positive solutions is implied. By using this non_existence result, blow_up estimates for a class quasi_linear reaction_diffusion systems (non_Newtonian filtration systems) are established, which extends the result of semi_linear reaction_diffusion(Fujita type) systems.