A problem with wear involving thermo-electro-viscoelastic materials

In this paper, we consider a mathematical model of a contact problem in thermo-electro-viscoelasticity. The body is in contact with an obstacle. The contact is frictional and bilateral with a moving rigid foundation which results in the wear of the contacting surface. We establish a variational formulation for the model and we prove the existence of a unique weak solution to the problem. The proof is based on a classical existence and uniqueness result on parabolic inequalities, differential equations and fixed point arguments. We present a variational formulation of the problem, and we prove the existence and uniqueness of the weak solution.