Subdifferential inclusions with unbounded perturbation: Existence and relaxation theorems
- 作者: Tolstonogov A.1
-
隶属关系:
- Institute of Dynamics and Control Theory, Siberian Branch
- 期: 卷 94, 编号 1 (2016)
- 页面: 396-400
- 栏目: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/223983
- DOI: https://doi.org/10.1134/S1064562416040116
- ID: 223983
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详细
The paper studies an evolution inclusion in a separable Hilbert space whose right-hand side contains the subdifferential of a proper convex lower semicontinuous function of time and a set-valued perturbation. Together with this inclusion, an inclusion with convexified perturbation values is considered. The existence and density of the solution set of the initial inclusion in the closure of the solution set of the inclusion with convexified perturbation are proved. This property is usually called relaxation. Traditional assumptions for relaxation theorems are the compactness property of the convex function and the boundedness of the perturbation. In the present paper, such assumptions are not made. Assumptions for subdifferential inclusions described by polyhedral sweeping processes and variational inequalities with time-dependent obstacles and constraints are specified.
作者简介
A. Tolstonogov
Institute of Dynamics and Control Theory, Siberian Branch
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Email: aatol@icc.ru
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