Optimal Decay Rate of Solutions to Timoshenko System with Past History in Unbounded Domains
Maisa KhaderPrincess Sumaya University of Technology, Amman, Jordan
Belkacem Said-HouariUniversity of Sharjah, Sharjah, United Arab Emirates
In this paper, we investigate the Cauchy problem for the Timoshenko system in thermo-elasticity, where the heat conduction is given by the Gurtin–Pipkin thermal law in one-dimensional space. We show an optimal decay rate of the -norm of the solution with the rate of which is better than found in . We also extend the recent results in  and  and showed that those results are only particular cases of the one obtained here. Also, we prove that the decay rate is controlled by a crucial stability number \alpha_g which depends on the parameters of the system.
Cite this article
Maisa Khader, Belkacem Said-Houari, Optimal Decay Rate of Solutions to Timoshenko System with Past History in Unbounded Domains. Z. Anal. Anwend. 37 (2018), no. 4, pp. 435–459DOI 10.4171/ZAA/1622