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On quasi-static contact problem with generalized Coulomb friction, normal compliance and damage†

Published online by Cambridge University Press:  09 November 2015

LESZEK GASIŃSKI  and
PIOTR KALITA
LESZEK GASIŃSKI
Affiliation:
Faculty of Mathematics and Computer Science, Jagiellonian University, Lojasiewicza 6, 30348 Krakow, Poland email: leszek.gasinski@ii.uj.edu.pl, piotr.kalita@ii.uj.edu.pl
PIOTR KALITA
Affiliation:
Faculty of Mathematics and Computer Science, Jagiellonian University, Lojasiewicza 6, 30348 Krakow, Poland email: leszek.gasinski@ii.uj.edu.pl, piotr.kalita@ii.uj.edu.pl
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Abstract

In this paper, we study a quasi-static frictional contact problem for a viscoelastic body with damage effect inside the body as well as normal compliance condition and multi-valued friction law on the contact boundary. The considered friction law generalizes Coulomb friction condition into multi-valued setting. The variational–hemi-variational formulation of the problem is derived and arguments of fixed point theory and surjectivity results for pseudo-monotone operators are applied, in order to prove the existence and uniqueness of solution.

Keywords

viscoelastic bodysub-differential frictional condition of Coulomb typedamagevariational inequalityhemi-variational inequality
Type
Papers
Information
European Journal of Applied Mathematics , Volume 27 , Issue 4 , August 2016 , pp. 625 - 646
Copyright
Copyright © Cambridge University Press 2015 

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Footnotes

†

The research was supported by the Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme under Grant Agreement No. 295118, the International Project co-financed by the Ministry of Science and Higher Education of Republic of Poland under grant no. W111/7.PR/2012 and the National Science Center of Poland under Maestro Advanced Project no. DEC-2012/06/A/ST1/00262 and the project Polonium Mathematical and Numerical Analysis for Contact Problems with Friction 2014/15 between the Jagiellonian University and Université de Perpignan Via Domitia.

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