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arXiv · 1811.01138

Long-Time Behavior of Quasilinear Thermoelastic Kirchhoff-Love Plates with Second Sound

Irena Lasiecka·Michael Pokojovy·Xiang Wan
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Abstract

We consider an initial-boundary-value problem for a thermoelastic Kirchhoff & Love plate, thermally insulated and simply supported on the boundary, incorporating rotational inertia and a quasilinear hypoelastic response, while the heat effects are modeled using the hyperbolic Maxwell-Cattaneo-Vernotte law giving rise to a 'second sound' effect. We study the local well-posedness of the resulting quasilinear mixed-order hyperbolic system in a suitable solution class of smooth functions mapping into Sobolev $H^{k}$-spaces. Exploiting the sole source of energy dissipation entering the system through the hyperbolic heat flux moment, provided the initial data are small in a lower topology (basic energy level corresponding to weak solutions), we prove a nonlinear stabilizability estimate furnishing global existence & uniqueness and exponential decay of classical solutions.

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Irena Lasiecka, Michael Pokojovy, Xiang Wan. 2018-11-03. Long-Time Behavior of Quasilinear Thermoelastic Kirchhoff-Love Plates with Second Sound. https://arxiv.org/abs/1811.01138

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