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.
Franca M., Johnson R. (2019). On the non-autonomous hopf bifurcation problem: Systems with rapidly varying coefficients. ELECTRONIC JOURNAL ON THE QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2019(56), 1-24 [10.14232/ejqtde.2019.1.56].
On the non-autonomous hopf bifurcation problem: Systems with rapidly varying coefficients
Franca M.
Membro del Collaboration Group
;
2019
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.File in questo prodotto:
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