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A new class of hyperbolic variational–hemivariational inequalities driven by non-linear evolution equations
Published online by Cambridge University Press: 16 March 2020
Abstract
The aim of the paper is to introduce and investigate a dynamical system which consists of a variational–hemivariational inequality of hyperbolic type combined with a non-linear evolution equation. Such a dynamical system arises in studies of complicated contact problems in mechanics. Existence, uniqueness and regularity of a global solution to the system are established. The approach is based on a new semi-discrete approximation with an application of a surjectivity result for a pseudomonotone perturbation of a maximal monotone operator. A new dynamic viscoelastic frictional contact model with adhesion is studied as an application, in which the contact boundary condition is described by a generalised normal damped response condition with unilateral constraint and a multivalued frictional contact law.
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- © The Author(s) 2020. Published by Cambridge University Press
Footnotes
This project has received funding from the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Skłodowska-Curie grant agreement no. 823731 CONMECH. It is supported by the National Science Center of Poland under Preludium project no. 2017/25/N/ST1/00611. The first author is also supported by the Natural Science Foundation of Guangxi grant no. 2018GXNSFAA281353 and the Ministry of Science and Higher Education of Republic of Poland under grants no. 4004/GGPJII/H2020/2018/0 and 440328/PnH2/2019. The work of the second author was partially supported by NSF under grant DMS-1521684.
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