Modelling of nonconvex nonsmooth energy problems. Dynamic hemivariational inequalities with impact effects

Nonconvex nonsmooth energy functions lead to hemivariational inequalities. The subjects of the present paper are dynamic hemivariational inequalities without and with impact effects. First some existence and approximation results are obtained for dynamic hemivariational inequalities without impact effects. Then for the case of impact a new type of variational expressions has been obtained including variations of the time and the place of impact and the corresponding dynamic hemivariational inequalities have been formulated.