Rong Hu, Mircea Sofonea
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.
Submitted August 19, 2021. Published January 6, 2022.
Math Subject Classifications: 35M86, 49J40, 47J20.
Key Words: History-dependent variational inequality; dual problem;
history-dependent inclusion; Tykhonov well-posedness; convergence results.
DOI: https://doi.org/10.58997/ejde.2022.03
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Rong Hu School of Mathematical Sciences University of Electronic Science and Technology of China Chengdu, Sichuan 611731, China email: hrong1130@foxmail.com |
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Mircea Sofonea Laboratoire de Math\'ematiques et Physique University of Perpignan Via Domitia 52 Avenue Paul Alduy, 66860 Perpignan, France email: sofonea@univ-perp.fr |
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