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Optimal energy decay for the wave-heat system on a rectangular domain

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Details

Original languageEnglish
Pages (from-to)808-819
Number of pages12
JournalSIAM JOURNAL ON MATHEMATICAL ANALYSIS
Volume51
Issue number2
DOIs
Publication statusPublished - 2019
Publication typeA1 Journal article-refereed

Abstract

We study the rate of energy decay for solutions of a coupled wave-heat system on a rectangular domain. Using techniques from the theory of C 0 -semigroups, and in particular a well-known result due to Borichev and Tomilov, we prove that the energy of classical solutions decays like t - 2/ 3 as t \rightarrow \infty . This rate is moreover shown to be sharp. Our result implies in particular that a general estimate in the literature, which predicts at least logarithmic decay and is known to be best possible in general, is suboptimal in the special case under consideration here. Our strategy of proof involves direct estimates based on separation of variables and a refined version of the technique developed in our earlier paper for a one-dimensional wave-heat system.

Keywords

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

Publication forum classification

Field of science, Statistics Finland