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July 2024 Asymptotic behavior of a viscoelastic problem with long-term memory and Tresca friction law
Mohamed Dilmi, Aissa Benseghir, Mourad Dilmi, Hamid Benseridi
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Hiroshima Math. J. 54(2): 133-155 (July 2024). DOI: 10.32917/h2022020

Abstract

This paper examines the asymptotic behavior of solutions of the three dimensional viscoelastic problem with long-term memory and Tresca friction law in a thin domain Σε. We study the asymptotic behavior of this problem when the thickness ε tends to zero and we prove a convergence theorem for the displacement and velocity in appropriate functional spaces. Besides, the limit problem with the limit of Tresca free boundary conditions and a specific Reynolds limit equation is obtained.

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Mohamed Dilmi. Aissa Benseghir. Mourad Dilmi. Hamid Benseridi. "Asymptotic behavior of a viscoelastic problem with long-term memory and Tresca friction law." Hiroshima Math. J. 54 (2) 133 - 155, July 2024. https://doi.org/10.32917/h2022020

Information

Received: 20 August 2022; Revised: 2 November 2023; Published: July 2024
First available in Project Euclid: 18 July 2024

Digital Object Identifier: 10.32917/h2022020

Subjects:
Primary: 35C20

Keywords: long-term memory , thin domain , Tresca friction law , viscoelastic problem , Weak solution

Rights: Copyright © 2024 Hiroshima University, Mathematics Program

Vol.54 • No. 2 • July 2024
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