Solutions of some nonlinear parabolic equations with initial blow-up
| dc.creator | Sayed, Waad Al | |
| dc.creator | Veron, Laurent | |
| dc.date | 2008-09-10 | |
| dc.date.accessioned | 2026-07-07T10:02:02Z | |
| dc.date.available | 2026-07-07T10:02:02Z | |
| dc.description | We study the existence and uniqueness of solutions of $\partial_tu-Δu+u^q=0$ ($q>1$) in $Ω\times (0,\infty)$ where $Ω\subset\mathbb R^N$ is a domain with a compact boundary, subject to the conditions $u=f\geq 0$ on $\partialΩ\times (0,\infty)$ and the initial condition $\lim_{t\to 0}u(x,t)=\infty$. By means of Brezis' theory of maximal monotone operators in Hilbert spaces, we construct a minimal solution when $f=0$, whatever is the regularity of the boundary of the domain. When $\partialΩ$ satisfies the parabolic Wiener criterion and $f$ is continuous, we construct a maximal solution and prove that it is the unique solution which blows-up at $t=0$. | |
| dc.identifier | https://arxiv.org/abs/0809.1805 | |
| dc.identifier | http://arxiv.org/abs/0809.1805 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168835 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35K60 | |
| dc.title | Solutions of some nonlinear parabolic equations with initial blow-up | |
| dc.type | text |