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

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Original languageEnglish
Pages (from-to)649–664
Number of pages16
JournalJournal of Evolution Equations
Issue number3
Publication statusPublished - Sep 2016
Publication typeA1 Journal article-refereed


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 simpler than the methods used by other authors in similar situations.

ASJC Scopus subject areas


  • C-semigroups, Coupled, Energy, Heat equation, Rates of decay, Resolvent estimates, Wave equation

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