Well-posedness of constrained evolutionary differential variational–hemivariational inequalities with applications

A system of a first order history-dependent evolutionary variational– hemivariational inequality with unilateral constraints coupled with a nonlinear ordinary differential equation in a Banach space is studied. Based on a fixed point theorem for history dependent operators, results on the well-posed...

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Bibliographic Details
Published inNonlinear analysis: real world applications Vol. 67; p. 103593
Main Author Migórski, Stanisław
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.10.2022
Subjects
Contact problem
Evolution triple
History-dependent operator
Unilateral constraint
Variational–hemivariational inequality
History-dependent operator
Contact problem
Unilateral constraint
Variational–hemivariational inequality
Evolution triple
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ISSN1468-1218
1878-5719
DOI10.1016/j.nonrwa.2022.103593

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Summary:A system of a first order history-dependent evolutionary variational– hemivariational inequality with unilateral constraints coupled with a nonlinear ordinary differential equation in a Banach space is studied. Based on a fixed point theorem for history dependent operators, results on the well-posedness of the system are proved. Existence, uniqueness, continuous dependence of the solution on the data, and the solution regularity are established. Two applications of dynamic problems from contact mechanics illustrate the abstract results. First application is a unilateral viscoplastic frictionless contact problem which leads to a hemivariational inequality for the velocity field, and the second one deals with a viscoelastic frictional contact problem which is described by a variational inequality.
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2022.103593