A. Amassad, K. L. Kuttler$, M. Rochdi and M. Shillor

We prove existence and uniqueness of the weak solution for a quasistatic
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.