Self-similar solutions of the p-Laplace heat equation: the case when p>2
| dc.creator | Bidaut-Véron, Marie-Françoise | |
| dc.date | 2009-02-13 | |
| dc.date.accessioned | 2026-07-07T12:41:36Z | |
| dc.date.available | 2026-07-07T12:41:36Z | |
| dc.description | We study the self-similar solutions of the equation \[ u_{t}-div(| \nabla u| ^{p-2}\nabla u)=0, \] in $\mathbb{R}^{N},$ when $p>2.$ We make a complete study of the existence and possible uniqueness of solutions of the form \[ u(x,t)=(\pm t)^{-α/β}w((\pm t)^{-1/β}| x|) \] of any sign, regular or singular at $x=0.$ Among them we find solutions with an expanding compact support or a shrinking hole (for $t>0),$ or a spreading compact support or a focussing hole (for $t<0).$ When $t<0,$ we show the existence of positive solutions oscillating around the particular solution $U(x,t)=C_{N,p}(| x| ^{p}/(-t))^{1/(p-2)}.$ | |
| dc.identifier | https://arxiv.org/abs/0902.2311 | |
| dc.identifier | http://arxiv.org/abs/0902.2311 | |
| dc.identifier | Proceedings of the Royal Society of Edinburg 139A (2009) 1-43 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/219827 | |
| dc.subject | Analysis of PDEs | |
| dc.title | Self-similar solutions of the p-Laplace heat equation: the case when p>2 | |
| dc.type | text |