Electron. J. Differential Equations, Vol. 2018 (2018), No. 151, pp. 1-26.

Stability of ground states for a nonlinear parabolic equation

Luca Bisconti, Matteo Franca

Abstract:
We consider the Cauchy-problem for the parabolic equation
$$ u_t = \Delta u+ f(u,|x|), $$
where $x \in \mathbb R^n$, $n >2$, and $f(u,|x|)$ 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.

Submitted April 5, 2018. Published August 10, 2018.
Math Subject Classifications: 35k58, 35k91, 34e05, 35b08, 35b35.
Key Words: Weak asymptotic stability; supercritical parabolic equations; ground states; asymptotic expansion.

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Luca Bisconti
Dipartimento di Matematica e Informatica "U. Dini"
Università degli Studi di Firenze
Via S. Marta 3, I-50139 Firenze, Italy
email: luca.bisconti@unifi.it
Matteo Franca
Dipartimento di Ingegneria Industriale e Scienze Matematiche
Università Politecnica delle Marche
Via Brecce Bianche, I-60131 Ancona, Italy
email: franca@dipmat.univpm.it

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