On a nonlinear parabolic problem: Stability properties of Ground States

Luca Bisconti; Matteo Franca

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arXiv · 1705.02164

On a nonlinear parabolic problem: Stability properties of Ground States

Luca Bisconti·Matteo Franca

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Abstract

We consider the Cauchy-problem for the following parabolic equation: \begin{equation*} \displaystyle u_t = \Delta u+ 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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Luca Bisconti, Matteo Franca. 2017-05-05. On a nonlinear parabolic problem: Stability properties of Ground States. https://arxiv.org/abs/1705.02164

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