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Using recent results in the theory of $C_0$-semigroups due to Batty, Chilland Tomilov (J. Eur. Math. Soc. 18(4):853-929, 2016) we study energy decay in aone-dimensional coupled wave-heat system with finite wave part and infiniteheat part. Our main result provides a sharp estimate for the rate of energydecay of a certain class of classical solutions. The present paper can bethought of as a natural sequel to a recent work by Batty, Paunonen and Seifert(J. Evol. Equ. 16:649-664, 2016), which studied a similar wave-heat system withfinite wave and heat parts using a celebrated result due to Borichev andTomilov.

Optimal energy decay in a one-dimensional wave-heat system with infinite heat part