  We investigate a quasi-static-antiplane contact problem, examining a
thermo-electro-visco-elastic material with a friction law dependent on the slip
rate, assuming that the foundation is electrically conductive. The mechanical
problem is represented by a system of partial differential equations, and
establishing its solution involves several key steps. Initially, we obtain a
variational formulation of the model, which comprises three systems: a
hemivariational inequality, an elliptic equation, and a parabolic equation.
Subsequently, we demonstrate the existence of a unique weak solution to the
model. The proof relies on various arguments, including those related to
evolutionary inequalities, techniques for decoupling unknowns, and certain
results from differential equations.
