Blow‐up estimates for a quasi‐linear reaction–diffusion system

In this paper, some sufficient conditions under which the quasilinear elliptic system ‐div(∣∇ u ∣ p‐2 ∇ u ) = u   m   1v   n   1, ‐div(∣∇ u ∣ q‐2 ∇ u ) = u   m   2v   n   2in ℝ N ( N ≥3) has no radially symmetric positive solution is derived. Then by using this non‐existence result, blow‐up estimates for a class of quasilinear reaction–diffusion systems u t = div (∣∇ u ∣ p‐2 ∇ u )+ u   m   1v   n   1,vt = div(∣∇ v ∣ q‐2 ∇ v ) + u   m   2v   n   2with the homogeneous Dirichlet boundary value conditions are obtained. Copyright © 2003 John Wiley & Sons, Ltd.