Large time behavior of solutions to the Cauchy problem for one-dimensional thermoelastic system with dissipation (Q1411811)

This paper studies the large-time behavior of smooth small solutions to the Cauchy problem for the one-dimensional thermoelastic system with dissipation (velocity-term) in the balance law of momentum. The global existence and time-decay rates of smooth small solutions are investigated in [\textit{S. Zheng}, {Chin. Ann. Math.}, Ser. B 8, 142--155 (1987; Zbl 0674.35012)] by applying the Fourier transform and the energy method. In this paper the authors improve the decay results in Zheng's paper by proving sharper time-decay properties, which seem to be optimal. The main ingredient in the proof is careful use of the energy method and the Green function method.