We consider the Cauchy-problem for the following parabolic equation: \begin{equation*} \displaystyle u_t = \Delta u+ f(u,|x|), \end{equation*} where $x \in \RR^n$, $n >2$, and $f=f(u,|x|)$ 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.
Stability of ground states for a nonlinear parabolic equation / Bisconti, Luca; Franca, Matteo. - In: ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 1072-6691. - ELETTRONICO. - 2018:(2018), pp. 1-26.
Stability of ground states for a nonlinear parabolic equation
Franca, Matteo
2018-01-01
Abstract
We consider the Cauchy-problem for the following parabolic equation: \begin{equation*} \displaystyle u_t = \Delta u+ f(u,|x|), \end{equation*} where $x \in \RR^n$, $n >2$, and $f=f(u,|x|)$ 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.File in questo prodotto:
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