Analysis of a dynamic electro-viscoelastic contact problem

In this work, we analyze a mathematical problem for dynamic contact between two electro-viscoelastic bodies with adhesion, normal compliance, and damage. An inclusion of the parabolic type describes the evolution of damage. A first-order differential equation explains the development of the bonding field. We create a variational formulation for the model and demonstrate the existence and uniqueness of the weak solution. Parabolic inequalities, variational inequalities, and the Banach fixed point theorem form the foundation for the proof.