Hemivariational inequality for a frictional contact problem in elasto-piezoelectricity

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November 2006, 6(6): 1339-1356. doi: 10.3934/dcdsb.2006.6.1339

Hemivariational inequality for a frictional contact problem in elasto-piezoelectricity

1.	Jagiellonian University, Faculty of Mathematics and Computer Science, Institute of Computer Science, ul. Nawojki 11, 30-072 Krakow, Poland

Received September 2005 Revised April 2006 Published August 2006

Abstract
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In this paper we study a class of inequality problems for static frictional contact between a piezoelastic body and a foundation. The constitutive law is assumed to be electrostatic and involves a nonlinear elasticity operator. The contact is described by Clarke subdifferential relations of nonmonotone and multivalued character in the normal and tangential directions on the boundary. We derive a variational formulation which is a coupled system of a hemivariational inequality and an elliptic equation. The existence of solutions to the model is a consequence of a more general result obtained from the theory of pseudomonotone mappings. Conditions under which a solution of the system is unique are also presented.

Keywords: piezoelectric, nonconvex, inclusion, frictional contact, existence and uniqueness., subdiffer-ential, hemivariational inequality.

Mathematics Subject Classification: Primary: 74M15, 47J20, 35J85, 74G25, 74G30; Sec-ondary: 35R70, 74F20, 49J4.

Citation: Stanislaw Migórski. Hemivariational inequality for a frictional contact problem in elasto-piezoelectricity. Discrete & Continuous Dynamical Systems - B, 2006, 6 (6) : 1339-1356. doi: 10.3934/dcdsb.2006.6.1339

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