Nishihara, Kenji; Nishibata, Shinya Large time behavior of solutions to the Cauchy problem for one-dimensional thermoelastic system with dissipation. (English) Zbl 1049.74020 J. Inequal. Appl. 6, No. 2, 167-189 (2001). 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. Reviewer: Song Jiang (Beijing) 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) Keywords:nonlinear thermoelasticity; one-dimensional model; Cauchy problem; time-decay rates; smooth small solutions Citations:Zbl 0674.35012 PDFBibTeX XMLCite \textit{K. Nishihara} and \textit{S. Nishibata}, J. Inequal. Appl. 6, No. 2, 167--189 (2001; Zbl 1049.74020) Full Text: DOI EuDML