Quasi-static thermoviscoelastic contact problem with slip dependent friction coefficient

We prove existence and uniqueness of the weak solution for a quasi-static thermoviscoelastic problem which describes bilateral frictional contact between a deformable body and a moving rigid foundation. Friction is modeled with slip rate dependent friction coefficient, and it may depend either on the current slip rate or on the accumulated slip over the contact history. The frictional heat generated in the process is taken into account. The proof is based on the existence of solutions for a regularized problem, a priori estimates and a fixed-point argument, which provides the solution when the friction coefficient is sufficiently small.