Well-posedness of constrained evolutionary differential variational–hemivariational inequalities with applications

A system of a first order history-dependent evolutionary variational-hemivariational inequality with unilateral constraints coupled nonlinear ordinary differential equation in Banach space is studied. Based on fixed point theorem for history dependent operators, results the well-posedness are proved. Existence, uniqueness, continuous dependence solution data, and regularity established. Two applications dynamic problems from contact mechanics illustrate abstract results. First application viscoplastic frictionless problem which leads to hemivariational velocity field, second one deals viscoelastic frictional described by variational inequality.