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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.
MSC:
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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