Abstract
In the paper we deliver a new existence and uniqueness result for a class of abstract nonlinear variational-hemivariational inequalities which are governed by two operators depending on the history of the solution, and include two nondifferentiable functionals, a convex and a nonconvex one. Then, we consider an initial boundary value problem which describes a model of evolution of a viscoelastic body in contact with a foundation. The contact process is assumed to be dynamic, and the friction is described by subdifferential boundary conditions. Both the constitutive law and the contact condition involve memory operators. As an application of the abstract theory, we provide a result on the unique weak solvability of the contact problem.
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Research supported by the Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme under Grant Agreement No. 295118 and the National Science Center of Poland under the Maestro Advanced Project No. DEC-2012/06/A/ST1/00262. The authors are also partially supported by the International Project co-financed by the Ministry of Science and Higher Education of Republic of Poland under Grant No. W111/7.PR/2012, and the project Polonium “Mathematical and Numerical Analysis for Contact Problems with Friction” 2014/15 between the Jagiellonian University in Krakow and Université de Perpignan Via Domitia.
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Migórski, S., Ogorzaly, J. Dynamic history-dependent variational-hemivariational inequalities with applications to contact mechanics. Z. Angew. Math. Phys. 68, 15 (2017). https://doi.org/10.1007/s00033-016-0758-4
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DOI: https://doi.org/10.1007/s00033-016-0758-4