Marius Cocou
Aix-Marseille University, Marseille, France

This work is concerned with the analysis of a class of dynamic contact problems with Coulomb friction between two thermoviscoelastic bodies with nonlinear elasticity and viscosity operators. The presented results extend to thermomechanical processes the unified approach used recently to solve some isothermal dynamic contact problems with complex boundary conditions including relaxed unilateral contact, pointwise friction, and adhesion. We study a mixed variational formulation given as an evolution system of two coupled nonlinear equations for which the Lagrange multipliers satisfy the contact constraints including the frictional heat generation condition. The existence of a strong solution is proved by using an equivalent fixed point problem for a multifunction, several estimates, and some existence results for variational equations.