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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
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1572-9176
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Volume 21, Issue 2

Issues

Dynamical contact problems with friction for hemitropic elastic solids

Avtandil Gachechiladze
  • A. Razmadze Mathematical Institute of I. Javakishvili Tbilisi State University, 6 Tamarashvili Str., Tbilisi 0177; and Department of Mathematics, Georgian Technical University, 77 M. Kostava Str., Tbilisi 0175, Georgia
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/ Roland Gachechiladze / David Natroshvili
  • Department of Mathematics, Georgian Technical University, 77 M. Kostava Str., Tbilisi 0175; and I. Vekua Institute of Applied Mathematics of I. Javakhishvili Tbilisi State University, 2 University Str., Tbilisi 0186, Georgia
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Published Online: 2014-05-01 | DOI: https://doi.org/10.1515/gmj-2014-0024

Abstract.

In the present paper we investigate a three-dimensional boundary-contact problem of dynamics for a homogeneous hemitropic elastic medium with regard to friction. We prove the uniqueness theorem using the corresponding Green formulas and positive definiteness of the potential energy. To analyze the existence of solutions we reduce equivalently the problem under consideration to a spatial variational inequality. We consider a special parameter-dependent regularization of this variational inequality which is equivalent to the relevant regularized variational equation depending on a real parameter and study its solvability by the Faedo–Galerkin method. Some a priori estimates for solutions of the regularized variational equation are established and with the help of an appropriate limiting procedure the existence theorem for the original contact problem with friction is proved.

Keywords: Elasticity theory; hemitropic solids; contact problem with friction; variational inequality; variational equation; Faedo–Galerkin method

MSC: 35J86; 49J40; 74M10; 74M15

About the article

Received: 2013-04-12

Revised: 2013-08-01

Accepted: 2013-09-03

Published Online: 2014-05-01

Published in Print: 2014-06-01


Citation Information: Georgian Mathematical Journal, Volume 21, Issue 2, Pages 165–185, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2014-0024.

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[1]
Avtandil Gachechiladze and Roland Gachechiladze
Transactions of A. Razmadze Mathematical Institute, 2016, Volume 170, Number 3, Page 363

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