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Analysis of a piezoelectric contact problem with subdifferential boundary condition

Published online by Cambridge University Press:  03 October 2014

Stanisław Migórski ,
Anna Ochal  and
Mircea Sofonea
Stanisław Migórski
Affiliation:
Faculty of Mathematics and Computer Science, Jagiellonian University, Institute of Computer Science, ul. Łojasiewicza 6, 30348 Krakow, Poland, (migorski@ii.uj.edu.pl)
Anna Ochal
Affiliation:
Faculty of Mathematics and Computer Science, Jagiellonian University, Institute of Computer Science, ul. Łojasiewicza 6, 30348 Krakow, Poland, (migorski@ii.uj.edu.pl)
Mircea Sofonea
Affiliation:
Laboratoire de Mathématiques et Physique, Université de Perpignan via Domitia, 52 Avenue Paul Alduy, 66860 Perpignan, France
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Abstract

We consider a mathematical model which describes the frictionless contact between a piezoelectric body and a foundation. The contact process is quasi-static and the foundation is assumed to be insulated. The novelty of the model consists in the fact that the material behaviour is described with an electro-elastic–visco-plastic constitutive law and the contact is modelled with a subdifferential boundary condition. We derive a variational formulation of the problem which is in the form of a system coupling two nonlinear integral equations with a history-dependent hemivariational inequality and a time-dependent linear equation. We prove the existence of a weak solution to the problem and, under additional assumptions, its uniqueness. The proof is based on a recent result on history-dependent hemivariational inequalities obtained by Migórski, Ochal and Sofonea in 2011.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 144 , Issue 5 , October 2014 , pp. 1007 - 1025
Copyright
Copyright © Royal Society of Edinburgh 2014 

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