Regularity of invariant sets in semilinear damped wave equations
| dc.creator | Prizzi, Martino | |
| dc.date | 2009-03-16 | |
| dc.date.accessioned | 2026-07-07T12:52:54Z | |
| dc.date.available | 2026-07-07T12:52:54Z | |
| dc.description | Under fairly general assumptions, we prove that every compact invariant subset $\mathcal I$ of the semiflow generated by the semilinear damped wave equation εu_{tt}+u_t+β(x)u-\sum_{ij}(a_{ij} (x)u_{x_j})_{x_i}&=f(x,u),&& (t,x)\in[0,+\infty[\timesΩ, u&=0,&&(t,x)\in[0,+\infty[\times\partialΩin $H^1_0(Ω)\times L^2(Ω)$ is in fact bounded in $D(\mathbf A)\times H^1_0(Ω)$. Here $Ω$ is an arbitrary, possibly unbounded, domain in $\R^3$, $\mathbf A u=β(x)u-\sum_{ij}(a_{ij}(x)u_{x_j})_{x_i}$ is a positive selfadjoint elliptic operator and $f(x,u)$ is a nonlinearity of critical growth. The nonlinearity $f(x,u)$ needs not to satisfy any dissipativeness assumption and the invariant subset $\mathcal I$ needs not to be an an attractor. | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/0903.2782 | |
| dc.identifier | http://arxiv.org/abs/0903.2782 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223448 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Dynamical Systems | |
| dc.subject | 35L70; 35B40; 35B65 | |
| dc.title | Regularity of invariant sets in semilinear damped wave equations | |
| dc.type | text |