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

Abstract

AbstractIn this paper, some sufficient conditions under which the quasilinear elliptic system ‐div(∣∇u∣p‐2∇u) = uv, ‐div(∣∇u∣q‐2∇u) = uv in ℝN(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 ut = div (∣∇u∣p‐2∇u)+uv,vt = div(∣∇v∣q‐2∇v) +uv with the homogeneous Dirichlet boundary value conditions are obtained. Copyright © 2003 John Wiley & Sons, Ltd.