Strong stabilization of models incorporating the thermoelastic Reissner-Mindlin plate equations with second sound. (English) Zbl 1228.35052
Instead of the exponential stability of a Timoshenko beam model, which is considered out-of date because the law of Cattaneo (instead of classical Fourier’s law), the author investigates the weaker property of strong stability for a Reissner-Mindlin plate system of thermoelasticity with second sound. Also, it is considered the following question: Is strong stability attainable for a three-dimensional structural acoustic model with two-dimensional Reissner-Mindlin thermoelastic plate interface with second sound? A common feature of both the plate model as well as the structural acoustic model is the novelty of complete hyperboliticity in the presence of thermal effects modelled by Cattaneo’s law instead of Fourier’s law. But, the resolvent of the generator of the underlying semigroup for the plate model is compact, whereas the resolvent operator for the structural acoustic model is not compact, due to the unbounded coupling of the wave dynamics in the acoustic chamber and the plate dynamics.
Reviewer: M. Marin (Brasov)
MSC:
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35L70 | Second-order nonlinear hyperbolic equations |
| 74K20 | Plates |
| 93D15 | Stabilization of systems by feedback |
| 74F05 | Thermal effects in solid mechanics |
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