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

Electronic Journal of Differential Equations

article

Rong Hu¹  Mircea Sofonea² 

[1] School of Mathematical Sciences University of Electronic Science and Technology of China Chengdu;Laboratoire de Math\'ematiques et Physique University of Perpignan Via Domitia 52 Avenue Paul Alduy

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

DOI  :  10.58997/ejde.2022.03

学科分类：数学（综合）

来源: Texas State University

【 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.

【 授权许可】

CC BY