Electron. J. Diff. Eqns., Vol. 2007(2007), No. 170, pp. 1-16.

A frictional contact problem for an electro-viscoelastic body

Zhor Lerguet, Meir Shillor, Mircea Sofonea

A mathematical model which describes the quasistatic frictional contact between a piezoelectric body and a deformable conductive foundation is studied. A nonlinear electro-viscoelastic constitutive law is used to model the piezoelectric material. Contact is described with the normal compliance condition, a version of Coulomb's law of dry friction, and a regularized electrical conductivity condition. A variational formulation of the model, in the form of a coupled system for the displacements and the electric potential, is derived. The existence of a unique weak solution of the model is established under a smallness assumption on the surface conductance. The proof is based on arguments of evolutionary variational inequalities and fixed points of operators.

Submitted February 12, 2007. Published December 4, 2007.
Math Subject Classifications: 74M10, 74M15, 74F15, 49J40.
Key Words: Piezoelectric; frictional contact; normal compliance; fixed point; variational inequality.

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Zhor Lerguet
Département de Matématiques, Faculté des Sciences
Université Farhat Abbas de Sétif
Cité Maabouda, 19000 Sétif, Algérie
email: zhorlargot@yahoo.fr
Meir Shillor
Department of Mathematics and Statistics
Oakland University
Rochester, MI 48309, USA
email: shillor@oakland.edu
Mircea Sofonea
Laboratoire de Mathématiques et Physique pour les Systémes,
University of Perpignan
52 avenue Paul Alduy
66860 Perpignan, France
email: sofonea@univ-perp.fr

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