  In this paper we prove 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 nonlinear constitutive viscoelastic law
with a long-term memory, which include the thermal effects and consider the
general nonmonotone and multivalued subdifferential boundary conditions for the
contact, friction and heat flux. The model consists of the system of the
hemivariational inequality of for the displacement and the parabolic
hemivariational inequality for the temperature. The existence of solutions is
proved by using recent results from the theory of hemivariational inequalities
and a fixed point argument.
