Well-posedness of a class of evolutionary variational–hemivariational inequalities in contact mechanics

Wei Xu; Weimin Han; Ting Li; Ziping Huang

doi:10.1016/j.cam.2024.116366

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Well-posedness of a class of evolutionary variational–hemivariational inequalities in contact mechanics

Journal article

Peer reviewed

Well-posedness of a class of evolutionary variational–hemivariational inequalities in contact mechanics

Wei Xu, Weimin Han, Ting Li and Ziping Huang

Journal of computational and applied mathematics, Vol.459, 116366

05/15/2025

DOI: 10.1016/j.cam.2024.116366

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Abstract

A class of evolutionary variational–hemivariational inequalities with a convex constraint is studied in this paper. An inequality in this class involves a first-order derivative and a history-dependent operator. Existence and uniqueness of a solution to the inequality is established by the Rothe method, in which the first-order temporal derivative is approximated by backward Euler’s formula, and the history-dependent operator is approximated by a modified left endpoint rule. The proof of the result relies on basic results in functional analysis only, and it does not require the notion of pseudomonotone operators and abstract surjectivity results for such operators, used in other papers on the Rothe method for other evolutionary variational–hemivariational inequalities. Moreover, a Lipschitz continuous dependence conclusion of the solution on the right-hand side is proved. Finally, a new frictional contact problem for viscoelastic material is discussed, which illustrates an application of the theoretical results.

Convex constraint

Existence and uniqueness

Frictional contact

Lipschitz continuous dependence

Rothe method

Variational–hemivariational inequality

Viscoelastic material

Details

Title: Subtitle: Well-posedness of a class of evolutionary variational–hemivariational inequalities in contact mechanics
Creators: Wei Xu - Tongji Zhejiang College
Weimin Han - University of Iowa
Ting Li - Tongji University
Ziping Huang - Tongji University
Resource Type: Journal article
Publication Details: Journal of computational and applied mathematics, Vol.459, 116366
DOI: 10.1016/j.cam.2024.116366
ISSN: 0377-0427
eISSN: 1879-1778
Publisher: Elsevier B.V; AMSTERDAM
Grant note: Tongji Zhejiang College: KY0221519
The authors thank the anonymous referees whose comments and suggestions lead to an improvement of the presentation of the paper. The work of Wei Xu is supported by the scientific research project of Tongji Zhejiang College under grant N0. KY0221519.
Language: English
Electronic publication date: 11/16/2024
Date published: 05/15/2025
Academic Unit: Mathematics
Record Identifier: 9984748155102771

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