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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


IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2018: 0.27

Online
ISSN
1572-9176
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Volume 21, Issue 4

Issues

Analysis and approximation of frictionless contact problems between two piezoelectric bodies with adhesion

Tedjani Hadj Ammar
  • Department of Mathematics, Faculty of Science and Technology, University of El-Oued, P.O. Box 789, 39000 El-Oued, Algeria
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/ Salah Drabla / Benyattou Benabderrahmane
Published Online: 2014-11-08 | DOI: https://doi.org/10.1515/gmj-2014-0044

Abstract

We consider a mathematical frictionless contact problem between two electro-elastic bodies. The contact is modelled with normal compliance and adhesion. We provide a variational formulation for the problem and prove the existence of a unique weak solution. The proofs are based on arguments of time-dependent variational inequalities, the Cauchy–Lipschitz Theorem and the Banach Fixed-Point Theorem. Then, a discrete scheme is introduced based on the finite element method to approximate the spatial variable. Furthermore, we provide optimal a priori error estimates for the displacements, the electric potential and the bonding at the contact interface.

Keywords: Piezoelectric material; adhesion; existence and uniqueness; fixed point; error estimates

MSC: 74M15; 74H20; 74H25

About the article

Received: 2013-02-03

Revised: 2013-05-15

Accepted: 2014-01-20

Published Online: 2014-11-08

Published in Print: 2014-12-01


Citation Information: Georgian Mathematical Journal, Volume 21, Issue 4, Pages 431–445, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2014-0044.

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