Asymptotic behavior of global solutions of the $u_t=Δu + u^{p}$
| dc.creator | Barraza, Oscar A. | |
| dc.creator | Langoni, Laura B. | |
| dc.date | 2008-01-30 | |
| dc.date.accessioned | 2026-07-07T08:57:26Z | |
| dc.date.available | 2026-07-07T08:57:26Z | |
| dc.description | We study the asymptotic behavior of nonnegative solutions of the semilinear parabolic problem {u_t=Δu + u^{p}, x\in\mathbb{R}^{N}, t>0 u(0)=u_{0}, x\in\mathbb{R}^{N}, t=0. It is known that the nonnegative solution $u(t)$ of this problem blows up in finite time for $1<p\leq 1+ 2/N$. Moreover, if $p> 1+ 2/N$ and the norm of $u_{0}$ is small enough, the problem admits global solution. In this work, we use the entropy method to obtain the decay rate of the global solution $u(t)$. | |
| dc.description | 15 | |
| dc.identifier | https://arxiv.org/abs/0801.4798 | |
| dc.identifier | http://arxiv.org/abs/0801.4798 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146970 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35B40; 35B35; 35K65; 35K55 | |
| dc.title | Asymptotic behavior of global solutions of the $u_t=Δu + u^{p}$ | |
| dc.type | text |