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• W1977244390 abstract "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 $gamma$ and $kappa$, 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." @default.
• W1977244390 created "2016-06-24" @default.
• W1977244390 creator A5015739982 @default.
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• W1977244390 date "2008-01-01" @default.
• W1977244390 modified "2023-09-27" @default.
• W1977244390 title "Long-time dynamics of a coupled system of nonlinear wave and thermoelastic plate equations" @default.
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• W1977244390 doi "https://doi.org/10.3934/dcds.2008.22.557" @default.
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