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

2019/09/02 by Ng, Abraham C. S.
#35B40 #35M33 #47D06 (34K30) #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1909.00801

Abstract

Harnessing the abstract power of the celebrated result due to Borichev and Tomilov (Math. Ann. 347:455--478, 2010, no. 2), we study the energy decay in a one-dimensional coupled wave-heat-wave system. We obtain a sharp estimate for the rate of energy decay of classical solutions by first proving a growth bound for the resolvent of the semigroup generator and then applying the asymptotic theory of C₀-semigroups. The present article can be naturally thought of as an extension of a recent paper by Batty, Paunonen, and Seifert (J. Evol. Equ. 16:649--664, 2016) which studied a similar wave-heat system via the same theoretical framework.

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