On the system of partial differential equations arising in mean field type control

Yves Achdou; Mathieu Laurière

doi:10.3934/dcds.2015.35.3879

Article Contents

2015, Volume 35, Issue 9: 3879-3900. Doi: 10.3934/dcds.2015.35.3879

This issue Previous Article Preface Next Article Ergodicity conditions for zero-sum games

On the system of partial differential equations arising in mean field type control

Yves Achdou^1, and
Mathieu Laurière^1,

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

Received: May 2014

Revised: September 2014

Published: May 2017

Abstract / Introduction Related Papers Cited by

Abstract

We discuss the system of Fokker-Planck and Hamilton-Jacobi-Bellman equations arising from the finite horizon control of McKean-Vlasov dynamics. We give examples of existence and uniqueness results. Finally, we propose some simple models for the motion of pedestrians and report about numerical simulations in which we compare mean filed games and mean field type control.

Keywords:

Mean field type control,
existence and uniqueness.

Mathematics Subject Classification: Primary: 49J20; Secondary: 35K55.

Citation:

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References

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