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History-dependent hemivariational inequalities with applications to Contact Mechanics. (English) Zbl 1399.49012

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.

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
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