Analysis for Unilateral Contact Problem with Coulomb's Friction in Thermo-Electro-Visco-Elasticity

The aim of this paper is to study a Signorini's problem with Coulomb's friction between a thermo-electro-viscoelasticity body and an electrically and thermally conductive foundation. The materiel's behavior is described by the linear thermo-electro-viscoelastic constitutive laws. The variational formulation is written as nonlinear quasivariational inequality for the displacement field, a nonlinear family elliptic variational equations for the electric potential and a nonlinear parabolic variational equations for the temperature field. We prove under some assumption existence of a weak solution to the problem. The thermo-electro-viscoelastic law with a some temperature parameter alpha > 0 is considered. Then we prove its unique solution as well as the convergence of its solution to the solution of the original problem as the temperature parameter alpha -> 0.