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Unbounded Second-Order State-Dependent Moreau’s Sweeping Processes in Hilbert Spaces

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Abstract

In this paper, an existence and uniqueness result of a class of second-order sweeping processes, with velocity in the moving set under perturbation in infinite-dimensional Hilbert spaces, is studied by using an implicit discretization scheme. It is assumed that the moving set depends on the time, the state and is possibly unbounded. The assumptions on the Lipschitz continuity and the compactness of the moving set, and the linear growth boundedness of the perturbation force are weaker than the ones used in previous papers.

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Acknowledgments

The authors would like to acknowledge the referees for their careful reading and insightful suggestions. The research of the second author is supported by Fondecyt Postdoc Project 3150332.

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Authors and Affiliations

  1. XLIM UMR-CNRS 7252, Université de Limoges, 87060, Limoges, France

    Samir Adly

  2. Centro de Modelamiento Matemático (CMM), Universidad de Chile, Santiago, Chile

    Ba Khiet Le

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  1. Samir Adly
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  2. Ba Khiet Le
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Correspondence to Samir Adly.

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Communicated by Nikolai Osmolovskii.

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Adly, S., Le, B.K. Unbounded Second-Order State-Dependent Moreau’s Sweeping Processes in Hilbert Spaces. J Optim Theory Appl 169, 407–423 (2016). https://doi.org/10.1007/s10957-016-0905-2

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  • DOI: https://doi.org/10.1007/s10957-016-0905-2

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