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Mean Field Type Control with Congestion

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Abstract

We analyze some systems of partial differential equations arising in the theory of mean field type control with congestion effects. We look for weak solutions. Our main result is the existence and uniqueness of suitably defined weak solutions, which are characterized as the optima of two optimal control problems in duality.

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Acknowledgments

The first author was partially funded by the ANR Projects ANR-12-MONU-0013 and ANR-12-BS01-0008-01. Both authors would like to thank A. Bensoussan for very helpful discussions.

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Authors and Affiliations

  1. Laboratoire Jacques-Louis Lions, UMR 7598, UPMC, CNRS, Univ. Paris Diderot, Sorbonne Paris Cité, 75205, Paris, France

    Yves Achdou & Mathieu Laurière

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  1. Yves Achdou
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  2. Mathieu Laurière
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Correspondence to Yves Achdou.

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In memory of A. V. Balakrishnan.

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Achdou, Y., Laurière, M. Mean Field Type Control with Congestion. Appl Math Optim 73, 393–418 (2016). https://doi.org/10.1007/s00245-016-9342-8

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  • DOI: https://doi.org/10.1007/s00245-016-9342-8

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