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arXiv · 2101.11397

Optimal decay for a wave-heat system with Coleman-Gurtin thermal law

Filippo Dell'Oro·Lassi Paunonen·David Seifert
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Abstract

We study the long-term behaviour of solutions to a one-dimensional coupled wave-heat system with Coleman-Gurtin thermal law. Our approach is based on the asymptotic theory of $C_0$-semigroups and recent results developed for coupled control systems. As our main results, we represent the system as a feedback interconnection between the wave part and the Coleman-Gurtin part and we show that the associated semigroup in the history framework of Dafermos is polynomially stable with optimal decay rate $t^{-2}$ as $t\to\infty$. In particular, we obtain a sharp estimate for the rate of energy decay of classical solutions to the problem.

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Filippo Dell'Oro, Lassi Paunonen, David Seifert. 2021-01-27. Optimal decay for a wave-heat system with Coleman-Gurtin thermal law. https://doi.org/10.1016/j.jmaa.2022.126706

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