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Large time behavior of solutions to the Cauchy problem for one-dimensional thermoelastic system with dissipation. (English) Zbl 1049.74020
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 [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.
74F05 Thermal effects in solid mechanics
74H40 Long-time behavior of solutions for dynamical problems in solid mechanics
35B40 Asymptotic behavior of solutions to PDEs
35M20 PDE of composite type (MSC2000)
35Q72 Other PDE from mechanics (MSC2000)
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