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

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2024-11-10 DOI:10.1016/j.cam.2024.116366

Wei Xu , Weimin Han , Ting Li , Ziping Huang

{"title":"Well-posedness of a class of evolutionary variational–hemivariational inequalities in contact mechanics","authors":"Wei Xu , Weimin Han , Ting Li , Ziping Huang","doi":"10.1016/j.cam.2024.116366","DOIUrl":null,"url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"459 ","pages":"Article 116366"},"PeriodicalIF":2.1000,"publicationDate":"2024-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0377042724006149","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

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.

查看原文本刊更多论文

接触力学中一类进化变分-半变分不等式的好求解性

本文研究了一类带有凸约束的进化变分-半变量不等式。该类不等式涉及一阶导数和历史依赖算子。不等式解的存在性和唯一性是通过罗特方法确定的，其中一阶时间导数是用后向欧拉公式逼近的，而与历史相关的算子是用修正的左端点规则逼近的。该结果的证明仅依赖于函数分析的基本结果，它不需要假单调算子的概念和此类算子的抽象可射性结果，而在其他关于罗特方法用于其他演化变分-求和不等式的论文中使用了这些概念和结果。此外，还证明了右侧解的 Lipschitz 连续依赖性结论。最后，讨论了一个新的粘弹性材料摩擦接触问题，说明了理论结果的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.