Applied Mathematics & Optimization

, Volume 73, Issue 3, pp 393–418 | Cite as

Mean Field Type Control with Congestion

Article

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.

Keywords

Mean field type control Weak solutions Optimal control 

Mathematics Subject Classification

35K40 35K55 35K65 35D30 49N70 49K20 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Laboratoire Jacques-Louis Lions, UMR 7598, UPMC, CNRSUniv. Paris Diderot, Sorbonne Paris CitéParisFrance

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