Optimal energy decay in a one-dimensional wave-heat system with infinite heat part

Using recent results in the theory of C0-semigroups due to Batty et al. (2016) [5] we study energy decay in a one-dimensional coupled wave-heat system with finite wave part and infinite heat part. Our main result provides a sharp estimate for the rate of energy decay of a certain class of classical...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2020-02, Vol.482 (2), p.123563, Article 123563
Main Authors: Ng, Abraham C.S., Seifert, David
Format: Article
Language:English
Subjects:
[formula omitted]-semigroups
Coupled
Energy decay
Heat equation
Resolvent estimates
Wave equation
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Summary:Using recent results in the theory of C0-semigroups due to Batty et al. (2016) [5] we study energy decay in a one-dimensional coupled wave-heat system with finite wave part and infinite heat part. Our main result provides a sharp estimate for the rate of energy decay of a certain class of classical solutions. The present paper can be thought of as a natural sequel to a recent work by Batty et al. (2016) [6], which studied a similar wave-heat system with finite wave and heat parts using a celebrated result due to Borichev and Tomilov.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2019.123563