Hemivariational inequalities in thermoviscoelasticity

In this paper we present the existence and uniqueness of the weak solution for a dynamic thermoviscoelastic problem which describes frictional contact between a body and a foundation. We employ the Kelvin-Voigt viscoelastic law which includes the thermal effects and consider the general nonmonotone and multivalued subdifferential boundary conditions. The model consists of the system of the hemivariational inequality of hyperbolic type for the displacement and the parabolic hemivariational inequality for the temperature. The existence of solutions is obtained from a surjectivity result for operators of pseudomonotone type. The uniqueness holds for a large class of operators of subdifferential type satisfying a relaxed monotonicity condition.