# American Institute of Mathematical Sciences

January  2008, 9(1): 129-143. doi: 10.3934/dcdsb.2008.9.129

## Noncoercive damping in dynamic hemivariational inequality with application to problem of piezoelectricity

 1 Department of Mathematics, Central South University, Changsha, Hunan 410076, China 2 Jagiellonian University, Faculty of Mathematics and Computer Science, Institute of Computer Science, ul. Nawojki 11, 30-072 Krakow

Received  October 2006 Revised  September 2007 Published  October 2007

In this paper we consider an evolution problem which model the frictional skin effects in piezoelectricity. The model consists of the system of the hemivariational inequality of hyperbolic type for the displacement and the time dependent elliptic equation for the electric potential. In the hemivariational inequality the viscosity term is noncoercive and the friction forces are derived from a nonconvex superpotential through the generalized Clarke subdifferential. The existence of weak solutions is proved by embedding the problem into a class of second order evolution inclusions and by applying a parabolic regularization method.
Citation: Zhenhai Liu, Stanislaw Migórski. Noncoercive damping in dynamic hemivariational inequality with application to problem of piezoelectricity. Discrete & Continuous Dynamical Systems - B, 2008, 9 (1) : 129-143. doi: 10.3934/dcdsb.2008.9.129
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