Duality arguments for well-posedness of history-dependent variational inequalities

Date

2022-01-06

Authors

Hu, Rong
Sofonea, Mircea

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

In this article we introduce a concept of dual problems in metric spaces. Then we state and prove an equivalence result concerning their well-posedness with respect to appropriate Tykhonov triples. We exemplify this result in the study of a history-dependent variational inequality with time-dependent constraints, for which the dual problem is in a form of a history-dependent inclusion. This allows us to deduce a convergence result which provides the continuous dependence of the solution with respect to the data. We end this paper with an example which represents an evidence of our abstract results.

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Keywords

History-dependent variational inequality, Dual problem, History-dependent inclusion, Tykhonov well-posedness, Convergence results

Citation

Hu, R., & Sofonea, M. (2022). Duality arguments for well-posedness of history-dependent variational inequalities. Electronic Journal of Differential Equations, 2022(03), pp. 1-10.

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Attribution 4.0 International

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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