A New System of Differential Quasi-Hemivariational Inequalities in Contact Mechanics.

In the paper we deal with a new class of systems of differential quasi-hemivariational inequalities. The system consists of a time-dependent constrained elliptic quasi-hemivariational inequality, an evolution quasi-hemivariational inequality and an ordinary differential equation in Banach spaces. The system is characterized by a strong coupling between the inequalities and the equation, presence of the unilateral constraint and history-dependent operators which leads to a complex time dependent dynamics. The result on the well posedness of the system is established via a surjectivity of multivalued pseudomonotone operators combined with a fixed point approach. The results find an application to a frictional quasistatic contact problem in mechanics with wear and thermal effects. [ABSTRACT FROM AUTHOR]