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References (30)
-
A. Sznitman (1991)
Topics in propagation of chaos -
R. Diperna, P. Lions (1989)
Ordinary differential equations, transport theory and Sobolev spacesInventiones mathematicae, 98
-
M. Hp (1966)
A class of markov processes associated with nonlinear parabolic equations.Proceedings of the National Academy of Sciences of the United States of America, 56
-
Y Achdou (2013)
Finite Difference Methods for Mean Field Games, Hamilton–Jacobi Equations: Approximations, Numerical Analysis and Applications -
Y. Achdou (2013)
Finite Difference Methods for Mean Field Games -
A. Bensoussan, J. Frehse, Phillip Yam (2013)
Mean Field Games and Mean Field Type Control Theory -
A. Bensoussan, J. Frehse (2013)
Control and nash games with mean field effectChinese Annals of Mathematics, Series B, 34
-
D. Gomes, Hiroyoshi Mitake (2015)
Existence for stationary mean-field games with congestion and quadratic HamiltoniansNonlinear Differential Equations and Applications NoDEA, 22
-
Wolfgang Hackbusch (2014)
Ordinary Differential Equations -
J. Lasry, P. Lions (2006)
Jeux à champ moyen. I – Le cas stationnaireComptes Rendus Mathematique, 343
-
A-S Sznitman (1991)
Topics in Propagation of Chaos, École d’Été de Probabilités de Saint-Flour XIX–1989 -
(2001)
Lecture Notes in Mathematics -
École Saint-Flour, D. Burkholder, É. Pardoux, A. Sznitman, P. Hennequin (1991)
Ecole d'été de probabilités de Saint-Flour XIX, 1989 -
R. Rockafellar, R. Rockafellar (1968)
Integrals which are convex functionals. IIPacific Journal of Mathematics, 24
-
(1997)
Convex analysis, Princeton Landmarks in Mathematics -
D. Gomes, Vardan Voskanyan (2015)
Short‐time existence of solutions for mean‐field games with congestionJournal of the London Mathematical Society, 92
-
Y. Achdou, M. Laurière (2015)
ON THE SYSTEM OF PARTIAL DIFFERENTIAL EQUATIONS ARISING IN MEAN FIELD TYPE CONTROLarXiv: Analysis of PDEs
-
D. Gomes, Hiroyoshi Mitake (2014)
Existence for stationary mean field games with quadratic Hamiltonians with congestionarXiv: Analysis of PDEs
-
P. Cardaliaguet, P. Graber, A. Porretta, D. Tonon (2014)
Second order mean field games with degenerate diffusion and local couplingNonlinear Differential Equations and Applications NoDEA, 22
-
R. Carmona, F. Delarue (2012)
Mean field forward-backward stochastic differential equationsElectronic Communications in Probability, 18
-
P. Hartman (1965)
Ordinary Differential EquationsJournal of the American Statistical Association, 60
-
P. Cardaliaguet, G. Carlier, B. Nazaret (2012)
Geodesics for a class of distances in the space of probability measuresCalculus of Variations and Partial Differential Equations, 48
-
P. Graber (2015)
Weak solutions for mean field games with congestionarXiv: Analysis of PDEs
-
Y. Achdou, G. Barles, 石井 仁司, G. Litvinov, P. Loreti, N. Tchou (2013)
Hamilton-Jacobi equations : approximations, numerical analysis and applications : Cetraro, Italy 2011 -
Cours du Coll`ege de France -
R. Carmona, F. Delarue, A. Lachapelle (2012)
Control of McKean–Vlasov dynamics versus mean field gamesMathematics and Financial Economics, 7
-
J. Lasry, P. Lions (2007)
Mean field gamesJapanese Journal of Mathematics, 2
-
D. Gomes, João Saúde (2013)
Mean Field Games Models—A Brief SurveyDynamic Games and Applications, 4
-
A. Porretta (2015)
Weak Solutions to Fokker–Planck Equations and Mean Field GamesArchive for Rational Mechanics and Analysis, 216
-
J. Lasry, P. Lions (2006)
Jeux à champ moyen. II – Horizon fini et contrôle optimalComptes Rendus Mathematique, 343
- Publisher
- Springer Journals
- Copyright
- Copyright © 2016 by Springer Science+Business Media New York
- Subject
- Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
- ISSN
- 0095-4616
- eISSN
- 1432-0606
- DOI
- 10.1007/s00245-016-9342-8
- Publisher site
- See Article on Publisher Site
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.
Journal
Applied Mathematics and Optimization – Springer Journals
Published: Jun 1, 2016