Instability of steady states for nonlinear wave and heat equations
| dc.creator | Karageorgis, Paschalis | |
| dc.creator | Strauss, Walter A. | |
| dc.date | 2006-11-18 | |
| dc.date.accessioned | 2026-07-07T07:33:05Z | |
| dc.date.available | 2026-07-07T07:33:05Z | |
| dc.description | We consider time-independent solutions of hyperbolic equations such as $\d_{tt}u -Δu= f(x,u)$ where $f$ is convex in $u$. We prove that linear instability with a positive eigenfunction implies nonlinear instability. In some cases the instability occurs as a blow up in finite time. We prove the same result for parabolic equations such as $\d_t u -Δu= f(x,u)$. Then we treat several examples under very sharp conditions, including equations with potential terms and equations with supercritical nonlinearities. | |
| dc.identifier | https://arxiv.org/abs/math/0611559 | |
| dc.identifier | http://arxiv.org/abs/math/0611559 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119335 | |
| dc.subject | Analysis of PDEs | |
| dc.title | Instability of steady states for nonlinear wave and heat equations | |
| dc.type | text |