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

[摘要] 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.

[学科分类] 数学（综合）

[关键词] History-dependent variational inequality;dual problem;history-dependent inclusion;Tykhonov well-posedness;convergence results.