OPTIMAL ENERGY DECAY FOR THE WAVE-HEAT SYSTEM ON A RECTANGULAR DOMAIN

被引：24

作者：

Batty, Charles ^{[1
]}

Paunonen, Lassi ^{[2
]}

Seifert, David ^{[1
]}

机构：

[1] St Johns Coll, Oxford OX1 3JP, England

[2] Tampere Univ Technol, Dept Math, POB 553, FIN-33101 Tampere, Finland

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2019年 / 51卷 / 02期

基金：

欧洲研究理事会; 芬兰科学院;

关键词：

wave equation; heat equation; coupled; rectangular domain; energy; rates of decay; C-0-semigroups; resolvent estimates; POLYNOMIAL DECAY; RATES; EQUATION;

D O I：

10.1137/18M1195796

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 -> infinity. 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.

引用

页码：808 / 819

页数：12

共 19 条

[1] THE MULTIDIMENSIONAL WAVE EQUATION WITH GENERALIZED ACOUSTIC BOUNDARY CONDITIONS II: POLYNOMIAL STABILITY [J].