  The paper studies the evolution of the thermomechanical and electric state of
a thermoviscoelastic thermistor that is in frictional contact with a reactive
foundation. The mechanical process is dynamic, while the electric process is
quasistatic. Friction is modeled with a nonmonotone relation between the
tangential traction and tangential velocity. Frictional heat generation is
taken into account and so is the strong dependence of the electric conductivity
on the temperature. The mathematical model for the process is in the form of a
system that consists of dynamic hyperbolic subdifferential inclusion for the
mechanical state coupled with a nonlinear parabolic equation for the
temperature and an elliptic equation for the electric potential. The paper
establishes the existence of a weak solution to the problem by using time
delays, a priori estimates and a convergence method.
