Asymptotic analysis for the elasticity system with Tresca and maximal monotone graph conditions

Volume 29, Issue 3, pp 252--263 https://doi.org/10.22436/jmcs.029.03.04

Publication Date: October 21, 2022 Submission Date: February 10, 2022 Revision Date: May 11, 2022 Accteptance Date: July 29, 2022

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Authors

M. Boudersa - Departement of mathematics, Unversity of Batna 2, Algeria. H. Benseridi - Departement of mathematics, Unversity of Setif 1, Algeria.

Abstract

In this paper, we consider the stationary problem in three dimensional thin domain \(\Omega ^{\varepsilon }\) with maximal monotone graph and Tresca conditions. In the first step, we present the problem statement and give the variational formulation. We then study the asymptotic behavior when one dimension of the domain tends to zero. In the latter case a specific Reynolds limit equation is obtained and the uniqueness of the displacement of the limit problem are proved.

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Keywords

• Asymptotic approach
• maximal monotone graph
• Tresca law
• variational problem
• weak solution

MSC

•  35R35
•  76F10
•  78M35

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