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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


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A quasistatic frictional contact problem for viscoelastic materials with long memory

Abderrezak Kasri
  • Corresponding author
  • Département de Mathématiques, Faculté des Sciences, Université 20 Août 1955 – Skikda, B.P. 26 Route El-Hadaiek Skikda, Algeria
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/ Arezki Touzaline
  • Laboratoire de Systèmes Dynamiques, Faculté de Mathématiques, USTHB, BP 32 El Alia, Bab-Ezzouar, 16111, Algeria
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Published Online: 2018-06-21 | DOI: https://doi.org/10.1515/gmj-2018-0002

Abstract

The aim of this paper is to study a quasistatic frictional contact problem for viscoelastic materials with long-term memory. The contact boundary conditions are governed by Tresca’s law, involving a slip dependent coefficient of friction. We focus our attention on the weak solvability of the problem within the framework of variational inequalities. The existence of a solution is obtained under a smallness assumption on a normal stress prescribed on the contact surface and on the coefficient of friction. The proof is based on a time discretization method, compactness and lower semicontinuity arguments.

Keywords: Viscoelasticity; long-term memory; Tresca’s law; slip dependent coefficient of friction,quasistatic; Rothe’s method; variational inequalities

MSC 2010: 49J40; 74M10; 74M15

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About the article

Received: 2015-10-30

Revised: 2016-11-21

Accepted: 2016-12-06

Published Online: 2018-06-21


Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2018-0002.

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