Variational analysis of a dynamic thermo-electro-viscoelastic contact problem with damage

In this paper, we present a thermodynamic problem involving a thermo-electro-viscoelastic body with contact damage and friction. The contact is characterized by a subdifferential condition. We formulate the mechanical problem and establish precise assumptions on the data to derive the variational formulation. Subsequently, we demonstrate the existence and uniqueness of the weak solution. The proof is grounded in a theorem pertaining to the existence and uniqueness of solutions for linear and nonlinear first-order evolution equations, complemented by a fixed-point argument.