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We study an abstract second order nonlinear evolution inclusion in a framework of evolution triple of spaces. We consider time-dependent possibly nonconvex nonsmooth functions and their Clarke subdifferentials operating on the unknown function. First we prove the existence of a weak solution. Then we study the asymptotic behavior of a sequence of solutions when a small parameter in the inertial term tends to zero. We prove that the limit function is a solution of a parabolic hemivariational inequality. Finally, we give an application of the abstract theorem to a quasi-static viscoelastic contact problem.
Migórski et al. (Thu,) studied this question.