A new partial differential system involving evolutionary variational-hemivariational inequalities arising in contact mechanics

This paper is devoted to the study of a new partial differential system involving an evolutionary variational inequality, a history-dependent hemivariational inequality and a partial differential equation in Banach spaces. Under mild conditions, by applying Banach’s fixed point theorem, we prove a unique solvability result for the problem. Furthermore, the main results are applied to obtain the unique solvability of a long-memory viscoelastic frictional contact problem that incorporates wear, damage, and a curved contact surface.