Well-posedness and optimal control for a dynamic thermo-viscoelastic signorini-type contact problem via the theory of variational–hemivariational inequalities

In this paper, we investigate control problems related to a mathematical model that describes dynamic Coulomb’s frictional contact between a thermo-viscoelastic body and a thermally conductive rigid foundation. The contact conditions and thermal conductivity on the contact surface are modeled using Signorini’s boundary conditions. We formulate the problem’s weak form as a system combining variational and hemivariational inequalities. Our study establishes the existence and uniqueness of a weak solution to the model, and under certain additional assumptions, demonstrates the continuous dependence of the solution with respect to the problem data. Furthermore, we address a class of optimal control problems and establish the existence of optimal solutions.