Journal of Inequalities and Applications
Volume 6 (2000), Issue 2, Pages 167-189
doi:10.1155/S1025583401000108
Large time behavior of solutions to the Cauchy problem for one-dimensional thermoelastic system with dissipation
1School of Political Science and Economics, Waseda University, Tokyo 169-8050, Japan
2Department of Mathematics, Fukuoka Institute of Technology, Fukuoka 811-0295, Japan
Received 2 August 1999; Revised 1 November 1999
Copyright © 2000 Kenji Nishihara and Shinya Nishibata. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In this paper we investigate the large time behavior of solutions to the Cauchy problem on R for a one-dimensional thermoelastic system with dissipation. When the initial data is suitably small, (S. Zheng, Chin. Ann. Math. 8B (1987), 142–155) established the global existence and the decay properties of the solution. Our aim is to improve the results and to obtain the sharper decay properties, which seems to be optimal. The proof is given by the energy method and the Green function method.