The Fujita Exponent for Semilinear Heat Equations with Quadratically Decaying Potential or in an Exterior Domain
| dc.creator | Pinsky, Ross G. | |
| dc.date | 2008-05-09 | |
| dc.date | 2008-05-13 | |
| dc.date.accessioned | 2026-07-07T09:38:11Z | |
| dc.date.available | 2026-07-07T09:38:11Z | |
| dc.description | Consider the equation u_t=Δu-Vu +au^p \text{in} R^n\times (0,T); u(x,0)=ϕ(x)\gneq0, \text{in} R^n, where $p>1$, $n\ge2$, $T\in(0,\infty]$, $V(x)\sim\fracω{|x|^2}$ as $|x|\to\infty$, for some $ω\neq0$, and $a(x)$ is on the order $|x|^m$ as $|x|\to\infty$, for some $m\in (-\infty,\infty)$. A solution to the above equation is called global if $T=\infty$. Under some additional technical conditions, we calculate a critical exponent $p^*$ such that global solutions exist for $p>p^*$, while for $1<p\le p^*$, all solutions blow up in finite time. We also show that when $V\equiv0$, the blow-up/global solution dichotomy for \eqref{abstract} coincides with that for the corresponding problem in an exterior domain with the Dirichlet boundary condition, including the case in which $p$ is equal to the critical exponent. | |
| dc.description | 24 pages, replaces and improves previous version | |
| dc.identifier | https://arxiv.org/abs/0805.1313 | |
| dc.identifier | http://arxiv.org/abs/0805.1313 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160717 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35K55, 35B33 | |
| dc.title | The Fujita Exponent for Semilinear Heat Equations with Quadratically Decaying Potential or in an Exterior Domain | |
| dc.type | text |