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

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• 作者：Charles Batty ; Lassi Paunonen ; David Seifert
• 关键词：Wave equation ; Heat equation ; Coupled ; Energy ; Rates of decay ; C0 ; semigroups ; Resolvent estimates
• 刊名：Journal of Evolution Equations
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：16
• 期：3
• 页码：649-664
• 全文大小：480 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  
• 出版者：Birkh盲user Basel
• ISSN：1424-3202
• 卷排序：16

文摘

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.