A new class of history-dependent quasi variational-hemivariational inequalities with constraints

doi:10.1016/j.cnsns.2022.106686

A new class of history-dependent quasi variational-hemivariational inequalities with constraints

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A new class of history-dependent quasi variational-hemivariational inequalities with constraints

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punktacja MEiN [2022]: 100

title:	A new class of history-dependent quasi variational-hemivariational inequalities with constraints
author:	Migórski Stanisław , Bai Yunru , Zeng Shengda
journal title:	Communications in Nonlinear Science and Numerical Simulation
volume:	114
date of publication :	2022
article ID:	106686
ISSN:	1007-5704
eISSN:	1878-7274
DOI:	10.1016/j.cnsns.2022.106686
language:	English
journal language:	English
abstract in English:	In this paper we consider an abstract class of time-dependent quasi variational–hemivariational inequalities which involves history-dependent operators and a set of unilateral constraints. First, we establish the existence and uniqueness of solution by using a recent result for elliptic variational–hemivariational inequalities in reflexive Banach spaces combined with a fixed-point principle for history-dependent operators. Then, we apply the abstract result to show the unique weak solvability to a quasistatic viscoelastic frictional contact problem. The contact law involves a unilateral Signorini-type condition for the normal velocity and the nonmonotone normal damped response condition while the friction condition is a version of the Coulomb law of dry friction in which the friction bound depends on the accumulated slip.
keywords in English:	variational–hemivariational inequality, history-dependent operator, unilateral constraint, existence and uniqueness, frictional contact
affiliation:	Wydział Matematyki i Informatyki : Katedra Teorii Optymalizacji i Sterowania, Wydział Matematyki i Informatyki
type:	journal article
subtype:	academic paper

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Except where otherwise noted, this item's license is described as Licencja Creative Commons - Uznanie autorstwa - Użycie niekomercyjne - Bez utworów zależnych 4.0 Międzynarodowa (CC BY-NC-ND)