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dc.contributor.authorSofonea, Mircea ( )
dc.contributor.authorXiao, Yi-Bin ( )
dc.date.accessioned2021-11-24T21:14:33Z
dc.date.available2021-11-24T21:14:33Z
dc.date.issued2019-05-10
dc.identifier.citationSofonea, M., & Xiao, Y. B. (2019). Tykhonov well-posedness of elliptic variational-hemivariational inequalities. Electronic Journal of Differential Equations, 2019(64), pp. 1-19.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/14952
dc.description.abstractWe consider a class of elliptic variational-hemivariational inequalities in an abstract Banach space for which we introduce the concept of well-posedness in the sense of Tykhonov. We characterize the well-posedness in terms of metric properties of a family of associated sets. Our results, which provide necessary and sufficient conditions for the well-posedness of inequalities under consideration, are valid under mild assumptions on the data. Their proofs are based on arguments of monotonicity, lower semicontinuity and properties of the Clarke directional derivative. For well-posed inequalities we also prove a continuous dependence result of the solution with respect to the data. We illustrate our abstract results in the study of one-dimensional examples, then we focus on some relevant particular cases, including variational-hemivariational inequalities with strongly monotone operators. Finally, we consider a model variational-hemivariational inequality which arises in Contact Mechanics for which we discuss its well-posedness and provide the corresponding mechanical interpretations.en_US
dc.formatText
dc.format.extent19 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2019, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectTykhonov well-posednessen_US
dc.subjectVariational-hemivariational inequalityen_US
dc.subjectApproximating sequenceen_US
dc.subjectContact problemen_US
dc.subjectUnilateral constrainten_US
dc.subjectFrictionen_US
dc.titleTykhonov well-posedness of elliptic variational-hemivariational inequalitiesen_US
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
dc.description.departmentMathematics


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