Existence and convergence results for evolution hemivariational inequalities

Abstract

In the paper we examine nonlinear evolution hemivariational inequality defined on a Gelfand fivefold of spaces. First we show that the problem with multivalued and $L$-pseudomonotone operator and zero initial data has a solution. Then the existence result is established in the case when the operator is single valued of Leray-Lions type and the initial condition is nonzero. Finally, the asymptotic behavior of solutions of hemivariational inequality with operators of divergence form is considered and the result on upper semicontinuity of the solution set is given.