The p-Laplace heat equation with a source term : self-similar solutions revisited
| dc.creator | Bidaut-Véron, Marie-Françoise | |
| dc.date | 2008-10-03 | |
| dc.date.accessioned | 2026-07-07T10:07:29Z | |
| dc.date.available | 2026-07-07T10:07:29Z | |
| dc.description | We study the self-similar solutions of any sign of the equation u_{t}-div(|∇u|^{p-2}∇u)=|u|^{q-1}u, in R^{N}, where p,q>1. We extend the results of Haraux-Weissler obtained for p=2 to the case q>p-1>0. In particular we study the existence of slow or fast decaying solutions. For given t>0, the fast solutions u(t,.) have a compact support in R^{N} when p>2, and |x|^{p/(2-p)}u(t,x) is bounded at infinity when p<2. We describe the behaviour for large |x| of all the solutions. According to the position of q with respect to the first critical exponent p-1+p/N and the critical Sobolev exponent q^{∗}, we study the existence of positive solutions, or the number of the zeros of u(t,.). We prove that any solution u(t,.) is oscillatory when p<2 and q is closed to 1. | |
| dc.identifier | https://arxiv.org/abs/0810.0654 | |
| dc.identifier | http://arxiv.org/abs/0810.0654 | |
| dc.identifier | advanced nonlinear studies 6, 1 (2006) 69-108 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170655 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35K60;35K65 | |
| dc.title | The p-Laplace heat equation with a source term : self-similar solutions revisited | |
| dc.type | text |