Stability of ground states for a nonlinear parabolic equation

Abstract

We consider the Cauchy-problem for the parabolic equation ut = ∆u + ƒ(u, |x|), where x ∈ ℝn, n > 2, and ƒ(u, |x|) is either critical or supercritical with respect to the Joseph-Lundgren exponent. In particular, we improve and generalize some known results concerning stability and weak asymptotic stability of positive ground states.