Duality arguments for well-posedness of history-dependent variational inequalities
Texas State University, Department of Mathematics
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.
History-dependent variational inequality, Dual problem, History-dependent inclusion, Tykhonov well-posedness, Convergence results
Hu, 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.
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