Migórski, Stanislaw; Ochal, Anna; Sofonea, Mircea History-dependent hemivariational inequalities with applications to Contact Mechanics. (English) Zbl 1399.49012 Ann. Univ. Buchar., Math. Ser. 4(62), No. 1, 193-212 (2013). Summary: In this paper, we survey some of our recent results on the existence and uniqueness of solutions to nonconvex and nonsmooth problems which arise in contact mechanics. The approach is based on operator subdifferential inclusions and hemivariational inequalities, and focuses on three aspects. First, we report on results on the second order history-dependent subdifferential inclusions and hemivariational inequalities; next, we discuss a class of stationary history-dependent operator inclusions and hemivariational inequalities; finally, we use these abstract results in the study of two viscoelastic contact problems with subdifferential boundary conditions. Cited in 1 Document MSC: 49J40 Variational inequalities 35A15 Variational methods applied to PDEs 35K85 Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators 35L86 Unilateral problems for nonlinear hyperbolic equations and variational inequalities with nonlinear hyperbolic operators 74M10 Friction in solid mechanics 74M15 Contact in solid mechanics 49S05 Variational principles of physics 35D30 Weak solutions to PDEs Keywords:history-dependent operator; evolutionary inclusion; hemivariational inequality; nonconvex potential; subdifferential mapping; frictional contact; viscoelastic material; weak solution PDFBibTeX XMLCite \textit{S. Migórski} et al., Ann. Univ. Buchar., Math. Ser. 4(62), No. 1, 193--212 (2013; Zbl 1399.49012)