The prior estimate and decay property of positive solutions are derived for
a system of quasi- linear elliptic differential equations first. Hence, th
e result of non-existence for differential equation system of radially noni
ncreasing positive solutions is implied. By using this nonexistence result,
blowup 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.