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 onedimensional coupled waveheatwave 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 C0semigroups. 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 waveheat system via the same theoretical framework.