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New decay rates for Cauchy problem of Timoshenko thermoelastic systems with past history: Cattaneo and Fourier law
  • Mounir Afilal,
  • Baowei Feng,
  • Abdelaziz Soufiyane
Mounir Afilal
Faculté Polydisciplinaire de Safi, Universite Cadi Ayyad
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Baowei Feng
Southwestern University of Finance and Economics
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Abdelaziz Soufiyane
University of Sharjah
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Abstract

In this paper, we investigate the decay properties of the thermoelastic Timoshenko system with past history in the whole space where the thermal effects are given by Cattaneo and Fourier laws. We obtain that both systems, Timoshenko-Fourier and Timoshenko-Cattaneo, have the same rate of decay (1+t)^{-(1/4)} and the regularity-loss type property is not present in some cases. Moreover, new stability number χ is introduced, such new number controls the decay rate of the solution with respect to the regularity of the initial data. To prove our results, we use the energy method in Fourier space to build an appropriate Lyapunov functionals that give the desired results.

Peer review status:ACCEPTED

31 Mar 2020Submitted to Mathematical Methods in the Applied Sciences
06 Apr 2020Submission Checks Completed
06 Apr 2020Assigned to Editor
07 Apr 2020Reviewer(s) Assigned
15 May 2020Review(s) Completed, Editorial Evaluation Pending
18 May 2020Editorial Decision: Revise Minor
19 May 20201st Revision Received
19 May 2020Submission Checks Completed
19 May 2020Assigned to Editor
19 May 2020Editorial Decision: Accept