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

Author: 

Batty, C
Paunonen, L
Seifert, D

Publication Date: 

26 March 2019

Journal: 

SIAM Journal on Mathematical Analysis

Last Updated: 

2020-10-21T05:34:18.9+01:00

Issue: 

2

Volume: 

51

DOI: 

10.1137/18M1195796

page: 

808-819

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 $t\to\infty$. 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.

Symplectic id: 

894519

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article