Title: An antiplane electro-elastic contact problem: case regularised friction law

Authors: Hacene-Chaouche Soumeya; Dalah Mohamed; Boudjedour Allaoua

Addresses: Faculty of Exact Sciences: FSE, Department of Mathematics, University Frères Mentouri Constantine 1, B.P. 325 Route Ain El Bey, Constantine 25017, Algeria ' Faculty of Exact Sciences: FSE, Department of Mathematics, University Frères Mentouri Constantine 1, Laboratory of Applied Mathematics and Modeling (LMAM): http://labomam.net/equipe5.html B.P. 325 Route Ain El Bey, Constantine 25017, Algeria ' Faculty of Exact Sciences: FSE, Department of Mathematics, University Frères Mentouri Constantine 1, B.P. 325 Route Ain El Bey, Constantine 25017, Algeria

Abstract: In this paper, we study an antiplane electro-elastic contact problem with regularised friction law. We suppose that the material is assumed to be electro-elastic and the foundation is assumed to be electrically conductive. In the first step, we write the mathematical model and its well-posedness. In the second step, we try to give the variational formulation and main results. Finally, we prove that the weak solution of the antiplane electro-elastic contact problem with regularised friction law is converge to the weak solution of problem P in Dalah et al. (2015) when the parameter of regularisation ρ is very small.

Keywords: regularised friction law; antiplane; friction law; variational formulation; variational inequality; weak solution.

DOI: 10.1504/IJDSDE.2019.103734

International Journal of Dynamical Systems and Differential Equations, 2019 Vol.9 No.4, pp.349 - 361

Received: 06 Feb 2018
Accepted: 13 Apr 2018

Published online: 22 Nov 2019 *

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