Long-time dynamics of a coupled system of nonlinear wave and thermoelastic plate equations
| dc.creator | Bucci, Francesca | |
| dc.creator | Chueshov, Igor | |
| dc.date | 2008-06-27 | |
| dc.date.accessioned | 2026-07-07T09:47:13Z | |
| dc.date.available | 2026-07-07T09:47:13Z | |
| dc.description | We prove the existence of a compact, finite dimensional, global attractor for a coupled PDE system comprising a nonlinearly damped semilinear wave equation and a nonlinear system of thermoelastic plate equations, without any mechanical (viscous or structural) dissipation in the plate component. The plate dynamics is modelled following Berger's approach; we investigate both cases when rotational inertia is included into the model and when it is not. A major part in the proof is played by an estimate--known as stabilizability estimate--which shows that the difference of any two trajectories can be exponentially stabilized to zero, modulo a compact perturbation. In particular, this inequality yields bounds for the attractor's fractal dimension which are independent of two key parameters, namely $γ$ and $κ$, the former related to the presence of rotational inertia in the plate model and the latter to the coupling terms. Finally, we show the upper semi-continuity of the attractor with respect to these parameters. | |
| dc.description | 38 pages. To appear in: Discrete Contin. Dyn. Syst. Series A | |
| dc.identifier | https://arxiv.org/abs/0806.4550 | |
| dc.identifier | http://arxiv.org/abs/0806.4550 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163794 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37L30, 35M20; 74H40 | |
| dc.title | Long-time dynamics of a coupled system of nonlinear wave and thermoelastic plate equations | |
| dc.type | text |