Hu, RongSofonea, Mircea2023-03-292023-03-292022-01-06Hu, R., & Sofonea, M. (2022). Duality arguments for well-posedness of history-dependent variational inequalities. <i>Electronic Journal of Differential Equations, 2022</i>(03), pp. 1-10.1072-6691https://hdl.handle.net/10877/16507In 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.Text10 pages1 file (.pdf)enAttribution 4.0 InternationalHistory-dependent variational inequalityDual problemHistory-dependent inclusionTykhonov well-posednessConvergence resultsArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.