Variational analysis of a dynamic electroviscoelastic problem with friction

A dynamic contact problem is considered in the paper. The material behavior is described by electro-visco-elastic constitutive law with piezoelectric effects. The body is in contact with a rigide obstacle. Contact is described with the Signorini condition, a version of Coulomb's law of dry friction, and with a regularized electrical conductivity condition. A variational formulation of the problem is derived. Under the assumption that coefficient of friction is small, existence and uniqueness of a weak solution of the problem is proved. The proof is based on evolutionary variational inequalities and fixed points of operators.