On a nonlinear parabolic problem: Stability properties of Ground States

Abstract

We consider the Cauchy-problem for the following parabolic equation: \begin{equation*} \displaystyle u_t = Δu+ f(u,|x|), \end{equation*} where $x\in {\mathbb{R}}^n$, $n>2$, and $f=f(u,|x|)$ is either critical or supercritical with respect to the Joseph-Lundgren exponent. Using a new unifying approach we extend to a larger class of nonlinear potentials $f$, some known results concerning stability and weak asymptotic stability of positive Ground States.

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