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arXiv · 1901.01423

Cauchy problem for thermoelastic plate equations with different damping mechanisms

Wenhui Chen
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Abstract

In this paper we study Cauchy problem for thermoelastic plate equations with friction or structural damping in $\mathbb{R}^n$, $n\geq1$, where the heat conduction is modeled by Fourier's law. We explain some qualitative properties of solutions influenced by different damping mechanisms. We show which damping in the model has a dominant influence on smoothing effect, energy estimates, $L^p-L^q$ estimates not necessary on the conjugate line, and on diffusion phenomena. Moreover, we derive asymptotic profiles of solutions in a framework of weighted $L^1$ data. In particular, sharp decay estimates for lower bound and upper bound of solutions in the $\dot{H}^s$ norm ($s\geq0$) are shown.

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Wenhui Chen. 2019-01-05. Cauchy problem for thermoelastic plate equations with different damping mechanisms. https://doi.org/10.4310/cms.2020.v18.n2.a7

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