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Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 15
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Research Article

Stability of Timoshenko system coupled with thermal law of Gurtin-Pipkin affecting on shear force

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Pages 5171-5192 | Received 01 Feb 2020, Accepted 24 Jan 2021, Published online: 05 Feb 2021
 

ABSTRACT

In this paper, we consider a Timoshenko type system coupled with parabolic equation that represents the thermal effect given by the Gurtin-Pipkin law while taking into account that the temperature influences on the shear force. We establish the global existence of solution the behavior of the solution. We also prove the lack of the exponential stability when ξ0, we obtain the exponential stability in the case where ξ=0 and the parameter p = 1 and also the polynomial stability in the case where ξ0 and 1<p<32 such that p is a parameter related to the thermal memory. One of the novel contribution here is that there is a new number ξ that is different from the number of stability that has been proven previously.

2010 Mathematics Subject Classifications:

Acknowledgments

The authors express sincere thanks to the editors and referees for their constructive comments and suggestions that helped to improve this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Hanni Dridi was supported by the Directorate General for Scientific Research and Technological Development (DGRSDT). Baowei Feng was supported by the National Natural Science Foundation of China [grant number 11701465]. Khaled Zennir thanks Deanship of Scientific Research, Qassim University, for its continuous support.

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