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

Tutkimustuotosvertaisarvioitu

Yksityiskohdat

AlkuperäiskieliEnglanti
Sivut808-819
Sivumäärä12
JulkaisuSIAM JOURNAL ON MATHEMATICAL ANALYSIS
Vuosikerta51
Numero2
DOI - pysyväislinkit
TilaJulkaistu - 2019
OKM-julkaisutyyppiA1 Alkuperäisartikkeli

Tiivistelmä

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.

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