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Boundary hemivariational inequalities of hyperbolic type and applications. (English) Zbl 1089.49014

The author establishes two important existence results for dynamic hemivariational inequalities of hyperbolic type with multidimensional potential laws. The basic tool in the proofs is a surjectivity result involving pseudomonotone operators. The method of proof consists in transforming the problems in evolution inclusions of first order with regular data and then by using a priori estimates to pass to the limit for achieving the conclusions. The author improves previous results by assuming less restrictive hypotheses on the locally Lipschitz functions generating the subdifferential relations. Applications to dynamic viscoelastic contact problems are also presented.

MSC:

49J40 Variational inequalities
47J20 Variational and other types of inequalities involving nonlinear operators (general)
74H20 Existence of solutions of dynamical problems in solid mechanics
35L85 Unilateral problems for linear hyperbolic equations and variational inequalities with linear hyperbolic operators
74M15 Contact in solid mechanics
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