Study of a Transmission Problem with Friction Law and Increasing Continuous Terms in a Thin Layer

Yasmina Kadri, Aissa Benseghir, Salah Boulaaras (), Hamid Benseridi and Mourad Dilmi
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Yasmina Kadri: Laboratory of Applied Mathematics, Faculty of Sciences, University Ferhat Abbas of Sétif 1, Sétif 19000, Algeria
Aissa Benseghir: Laboratory of Applied Mathematics, Faculty of Sciences, University Ferhat Abbas of Sétif 1, Sétif 19000, Algeria
Salah Boulaaras: Department of Mathematics, College of Science and Arts in ArRass, Qassim University, Buraydah 51452, Saudi Arabia
Hamid Benseridi: Laboratory of Applied Mathematics, Faculty of Sciences, University Ferhat Abbas of Sétif 1, Sétif 19000, Algeria
Mourad Dilmi: Laboratory of Applied Mathematics, Faculty of Sciences, University Ferhat Abbas of Sétif 1, Sétif 19000, Algeria

Mathematics, 2023, vol. 11, issue 22, 1-18

Abstract: The aim of this paper is to establish the asymptotic analysis of nonlinear boundary value problems. The non-stationary motion is given by the elastic constructive law. The contact is described with a version of Tresca’s law of friction. A variational formulation of the model, in the form of a coupled system for the displacements and the nonlinear source terms, is derived. The existence of a unique weak solution of the model is established. We also give the problem in transpose form, and we demonstrate different estimates of the displacement and of the source term independently of the small parameter. The main corresponding convergence results are stated in the different theorems of the last section.

Keywords: dynamic regime; elastic bodies; frictionless contact; mathematical operators; Newtonian fluids; partial differential equations; Tresca law; variational inequalities (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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