Optimal Control of a New Class of Parabolic Quasi Variational–Hemivariational Inequality

The primary objective of this paper is to study a new class of parabolic quasi variational–hemivariational inequalities. First, we prove a unique solvability result for such class under some mild conditions. Second, we show the existence of an optimal solution for an associated control problem. Finally, these results are applied to a model of quasistatic frictional contact in mechanics.