EXISTENCE OF SOLUTIONS TO A THERMO-VISCOELASTIC CONTACT PROBLEM WITH COULOMB FRICTION

Abstract

A thermo-viscoelastic contact problem with Coulomb friction is studied. The model involves a temperature-dependent heat conductivity with moderate growth in order to control the rapidly growing mixed terms as e.g. the heat generated by friction or by viscous deformation. The contact condition is formulated in velocities. The existence of a solution is proved by an approximation of the problem in several steps involving a penalty-approximation and a smoothing of the friction law. The solvability of the approximate problem is proved by the Galerkin method. A priori estimates uniform with respect to all approximation parameters make it possible to pass to the original problem. These estimates are based on a regularity result for the contact problem without heat transfer.