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Weak solvability of a piezoelectric contact problem†

Published online by Cambridge University Press:  01 April 2009

STANISŁAW MIGÓRSKI ,
ANNA OCHAL  and
MIRCEA SOFONEA
STANISŁAW MIGÓRSKI
Affiliation:
Faculty of Mathematics and Computer Science, Institute of Computer Science, Jagiellonian University, Nawojki 11, 30072 Krakow, Poland email: Stanislaw.Migorski@softlab.ii.uj.edu.pl; ochal@softlab.ii.uj.edu.pl
ANNA OCHAL
Affiliation:
Faculty of Mathematics and Computer Science, Institute of Computer Science, Jagiellonian University, Nawojki 11, 30072 Krakow, Poland email: Stanislaw.Migorski@softlab.ii.uj.edu.pl; ochal@softlab.ii.uj.edu.pl
MIRCEA SOFONEA
Affiliation:
Laboratoire de Mathématiques, Physique et Systèmes, Université de Perpignan, 52 Avenue Paul Alduy, 66860 Perpignan, France email: sofonea@univ-perp.fr
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Abstract

We consider a mathematical model which describes the frictional contact between a piezoelectric body and a foundation. The material behaviour is modelled with a non-linear electro-elastic constitutive law, the contact is bilateral, the process is static and the foundation is assumed to be electrically conductive. Both the friction law and the electrical conductivity condition on the contact surface are described with subdifferential boundary conditions. We derive a variational formulation of the problem which is of the form of a system of two coupled hemi-variational inequalities for the displacement and the electric potential fields, respectively. Then we prove the existence of a weak solution to the model and, under additional assumptions, its uniqueness. The proof is based on an abstract result on operator inclusions in Banach spaces.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 20 , Issue 2 , April 2009 , pp. 145 - 167
Copyright
Copyright © Cambridge University Press 2008

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