Optimal energy decay in a one-dimensional coupled wave–heat system

Journal article

We study a simple one-dimensional coupled wave–heat system and obtain a sharp estimate for the rate of energy decay of classical solutions. Our approach is based on the asymptotic theory of C0-semigroups and in particular on a result due to Borichev and Tomilov (Math Ann 347:455–478, 2010), which reduces the problem of estimating the rate of energy decay to finding a growth bound for the resolvent of the semigroup generator. This technique not only leads to an optimal result, it is also simpl...

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Authors: Batty, C; Paunonen, L; Seifert, D

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer International Publishing Publisher's website
• Journal: Journal of Evolution Equations Journal website
• Volume: 16
• Issue: 3
• Pages: 649–664
• Publication date: 2016-01-01
• EISSN: 11424-3202
• ISSN: 1424-3199
• Keywords: resolvent estimates; wave equation; C0-semigroups; heat equation; energy; coupled; rates of decay