A convergence criterion for elliptic variational inequalities

IF 1.1 4区数学 Q2 MATHEMATICS, APPLIED

Applicable Analysis Pub Date : 2023-10-16 DOI:10.1080/00036811.2023.2268636

Claudia Gariboldi, Anna Ochal, Mircea Sofonea, Domingo A. Tarzia

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引用次数: 0

Abstract

AbstractWe consider an elliptic variational inequality with unilateral constraints in a Hilbert space X which, under appropriate assumptions on the data, has a unique solution u. We formulate a convergence criterion to the solution u, i.e. we provide necessary and sufficient conditions on a sequence {un}⊂X which guarantee the convergence un→u in the space X. Then we illustrate the use of this criterion to recover well-known convergence results and well-posedness results in the sense of Tykhonov and Levitin–Polyak. We also provide two applications of our results, in the study of a heat transfer problem and an elastic frictionless contact problem, respectively.Keywords: Elliptic variational inequalityconvergence criterionconvergence resultswell-posednesscontactheat transferunilateral constraint2010 MSC: 47J2049J4040A0574M1574M1035J20 AcknowledgmentsThis project has received funding from the European Union's Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant Agreement No. 823731 CONMECH. The second author was also supported by the Ministry of Science and Higher Education of Republic of Poland under Grant No. 440328/PnH2/2019, and in part from National Science Centre, Poland under project OPUS no. 2021/41/B/ST1/01636.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work was supported by European Commission[].

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椭圆型变分不等式的收敛准则

摘要考虑Hilbert空间X中具有单侧约束的椭圆型变分不等式，在适当的数据假设下，具有唯一解u，并给出了解u的收敛准则。即，我们给出序列{un}≠X在空间X中收敛un→u的充分必要条件，然后我们举例说明使用这个判据来恢复众所周知的Tykhonov和Levitin-Polyak意义上的收敛结果和适定性结果。我们还提供了两个应用我们的结果，在研究传热问题和弹性无摩擦接触问题，分别。关键词:椭圆变分不等式收敛准则收敛结果稳定接触转移单边约束2010 MSC: 47J2049J4040A0574M1574M1035J20致谢本项目已获得欧盟地平线2020研究与创新计划资助，Marie Sklodowska-Curie资助协议No. 823731 CONMECH。第二作者还得到了波兰共和国科学和高等教育部(资助号440328/PnH2/2019)的支持，并部分得到了波兰国家科学中心(项目OPUS No. 2019)的支持。2021/41 / B / ST1/01636。披露声明作者未报告潜在的利益冲突。本研究得到了欧盟委员会的支持[]。

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来源期刊

Applicable Analysis 数学-应用数学

CiteScore

2.60

自引率

9.10%

发文量

175

审稿时长

2 months

期刊介绍： Applicable Analysis is concerned primarily with analysis that has application to scientific and engineering problems. Papers should indicate clearly an application of the mathematics involved. On the other hand, papers that are primarily concerned with modeling rather than analysis are outside the scope of the journal General areas of analysis that are welcomed contain the areas of differential equations, with emphasis on PDEs, and integral equations, nonlinear analysis, applied functional analysis, theoretical numerical analysis and approximation theory. Areas of application, for instance, include the use of homogenization theory for electromagnetic phenomena, acoustic vibrations and other problems with multiple space and time scales, inverse problems for medical imaging and geophysics, variational methods for moving boundary problems, convex analysis for theoretical mechanics and analytical methods for spatial bio-mathematical models.