JournalszaaVol. 37, No. 4pp. 435–459

Optimal Decay Rate of Solutions to Timoshenko System with Past History in Unbounded Domains

  • Maisa Khader

    Princess Sumaya University of Technology, Amman, Jordan
  • Belkacem Said-Houari

    University of Sharjah, Sharjah, United Arab Emirates
Optimal Decay Rate of Solutions to Timoshenko System with Past History in Unbounded Domains cover
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Abstract

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 L2L^2-norm of the solution with the rate of (1+t)1/8(1 + t)^{-1/8} which is better than (1+t)1/12(1 + t)^{-1/12} found in [6]. We also extend the recent results in [7] and [8] 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. 435–459

DOI 10.4171/ZAA/1622