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

• 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.
Mathematics Subject Classification: Primary: 35L85, 35L70, 34G25; Secondary: 74H20, 74F15, 74M10.

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