Glasnik Matematicki, Vol. 43, No.1 (2008), 137-158.

FRICTIONAL CONTACT PROBLEM IN DYNAMIC ELECTROELASTICITY

Mostafa Kabbaj and El-H. Essoufi

Département de Mathématiques, Faculté des Sciences et Techniques, Universitée Hassan Premier, Km 3, route Casablanca, B.P. 577, Settat, Maroc
e-mail: essoufi@gmail.com

Abstract.   The dynamic evolution with frictional contact of a electroelastic body is considered. In modelling the contact, the Tresca model is used. We derive a variational formulation for the model in a form of a coupled system involving the displacement and the electric potential fields. We provide existence and uniqueness result. The proof is based on a regularization method, Galerkin method, compactness and lower semicontinuity arguments. Such a result extend the result obtained by Duvaut and Lions, where the analysis of friction in dynamic elasticity materials was provided. The novelty of this paper consists in the fact that here we take into account the piezoelectric properties of the materials.

2000 Mathematics Subject Classification.   35J20, 37L65, 46B50, 49J40, 65F22, 74H20, 74H25.

Key words and phrases.   Dynamic electroelasticity, second-order hyperbolic variational inequality, regularization method, Faedo-Galerkin method, compactness method, existence, uniqueness.

DOI: 10.3336/gm.43.1.10

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