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All issues Volume 29 (2023) ESAIM: COCV, 29 (2023) 29 References
Open Access
Issue
ESAIM: COCV
Volume 29, 2023
Article Number 29
Number of page(s) 38
DOI https://doi.org/10.1051/cocv/2023024
Published online 27 April 2023
  1. Y. Achdou and M. Laurière, On the system of partial differential equations arising in mean field type control. Disc. Cont. Dyn. Syst. 35 (2015) 3879–3900. [Google Scholar]
  2. L. Ambrosio, N. Gigli and G. Savaré, Gradient Flows in Metric Spaces and in the Space of Probability Measures. Lectures in Mathematics ETH Zürich. Birkhäuser Verlag (2008). [Google Scholar]
  3. F. Antonelli, Backward-forward stochastic differential equations. Ann. Appl. Probab. 3 (1993) 777–793. [Google Scholar]
  4. R. Axelrod, The Evolution of Cooperation: Revised Edition. Basic Books (2009). [Google Scholar]
  5. M. Bardi and M. Fischer, On non-uniqueness and uniqueness of solutions in finite-horizon mean field games. ESAIM: COCV 25 (2019) 44. [CrossRef] [EDP Sciences] [Google Scholar]
  6. N. Bellomo, P. Degond and E. Tadmor, Active Particles, Vol. 1: Advances in Theory, Models, and Applications. Birkhauser (2017). [Google Scholar]
  7. A. Bensoussan, J. Frehse and P. Yam, Mean Field Games and Mean Field Type Control Theory, Vol. 101. Springer (2013). [CrossRef] [Google Scholar]
  8. A. Bensoussan, K.C.J. Sung, S.C.P. Yam and S.-P. Yung, Linear-quadratic mean field games. J. Optim. Theory Appl. 169 (2016) 496–529. [Google Scholar]
  9. S. Bianchini and A. Bressan, Vanishing viscosity solutions of nonlinear hyperbolic systems. Ann. of Math. 161 (2005) 223–342. [Google Scholar]
  10. V.I. Bogachev, Measure Theory, Vol. 2. Springer-Verlag, Berlin, Heidelberg (2007). [CrossRef] [Google Scholar]
  11. M. Bongini, M. Fornasier, F. Rossi and F. Solombrino, Mean Field Pontryagin Maximum Principle. J. Optim. Theory Applic. 175 (2017) 1–38. [Google Scholar]
  12. B. Bonnet, A Pontryagin maximum principle in Wasserstein spaces for constrained optimal control problems. ESAIM COCV 25 (2019) 52. [CrossRef] [EDP Sciences] [Google Scholar]
  13. B. Bonnet and H. Frankowska, Differential inclusions in Wasserstein spaces: the Cauchy-Lipschitz framework. J. Diff. Eq. 271 (2021) 594–637. [Google Scholar]
  14. B. Bonnet and F. Rossi, The Pontryagin maximum principle in the Wasserstein space. Calc. Variat. Partial Diff. Eq. 58 (2019) 11. [Google Scholar]
  15. B. Bonnet and F. Rossi, Intrinsic Lipschitz regularity of mean-field optimal controls. SIAM J. Control Optim. 59 (2021) 2011–2046. [Google Scholar]
  16. M. Burger, R. Pinnau, O. Totzeck, O. Tse and A. Roth, Instantaneous control of interacting particle systems in the mean-field limit. J. Comput. Phys. 405 (2020) 109181. [Google Scholar]
  17. S. Camazine, J.-L. Deneubourg, N.R. Franks, J. Sneyd, G. Theraulaz and E. Bonabeau, Self-Organization in Biological Systems. Princeton University Press (2001). [Google Scholar]
  18. M. Caponigro, M. Fornasier, B. Piccoli and E. Trelat, Sparse stabilization and control of alignment models. Math. Mod. Meth. Appl. Sci. 25 (2015) 521–564. [Google Scholar]
  19. P. Cardaliaguet, P. Jameson Graber, A. Porretta and D. Tonon, Second order mean field games with degenerate diffusion and local coupling. Nonlinear Diff. Eq. Appl. 22 (2015) 1287–1317. [Google Scholar]
  20. R. Carmona and F. Delarue, Mean field forward-backward stochastic differential equations. Electron. Commun. Probab. 18 (2013) 1–15. [Google Scholar]
  21. R. Carmona and F. Delarue, Forward-backward stochastic differential equations and controlled McKean-Vlasov dynamics. Ann. Probab. 43 (2015) 2647–2700. [Google Scholar]
  22. R. Carmona and F. Delarue, Probabilistic theory of mean field games with applications I. Vol. 83 of Probability Theory and Stochastic Modelling. Springer (2018). [Google Scholar]
  23. R. Carmona and F. Delarue, Probabilistic theory of mean field games with applications II. Vol. 84 of Probability Theory and Stochastic Modelling. Springer (2018). [Google Scholar]
  24. G. Cavagnari, A. Marigonda, K.T. Nguyen and F.S. Priuli, Generalized control systems in the space of probability MEASURES. Set-Valued Var. Anal. 26 (2018) 663–691. [Google Scholar]
  25. G. Cavagnari, A. Marigonda and B. Piccoli, Generalized dynamic programming principle and sparse mean-field control problems. J. Math. Anal. Applic. 481 (2020) 123437. [Google Scholar]
  26. J.F. Chassagneux, D. Crisan and F. Delarue, A probabilistic approach to classical solutions of the master equation for large population equilibria. Mem. Am. Math. Soc. 280 (2022). [Google Scholar]
  27. J.-Y. Chemin. A remark on the inviscid limit for two-dimensional incompressible fluids. Commun. Part. Diff. Eq. 21 (1996) 1771–1779. [Google Scholar]
  28. G. Ciampa, G. Crippa and S. Spirito, Strong convergence of the vorticity for the 2D Euler equations in the inviscid limit. Arch. Rational Mech. Anal. 240 (2021) 295–326. [Google Scholar]
  29. G. Ciampa and F. Rossi, Vanishing viscosity for linear-quadratic mean-field control problems. IEEE 60th Annual Conference on Decision and Control (CDC) (2021) 185–190. [Google Scholar]
  30. E. Cristiani, B. Piccoli and A. Tosin, Multiscale Modeling of Pedestrian Dynamics, Vol. 12. Springer (2014). [CrossRef] [Google Scholar]
  31. M. Duprez, M. Morancey and F. Rossi. Approximate and exact controllability of the continuity equation with a localized vector field. SIAM J. Control Optim. 57 (2019) 1284–1311. [Google Scholar]
  32. M. Duprez, M. Morancey and F. Rossi, Minimal time for the continuity equation controlled by a localized perturbation of the velocity vector field. J. Diff. Eq. 269 (2020) 82–124. [Google Scholar]
  33. M. Fornasier, S. Lisini, C. Orrieri and G. Savare, Mean-field optimal control as gamma-limit of finite agent controls. Eur. J. Appl. Math. 30 (2019) 1153–1186. [Google Scholar]
  34. M. Fornasier, B. Piccoli and F. Rossi, Mean-field sparse optimal control. Phil. Trans. R. Soc. A 372 (2014) 20130400. [CrossRef] [PubMed] [Google Scholar]
  35. M. Fornasier and F. Solombrino, Mean field optimal control. Esaim COCV 20 (2014) 1123–1152. [CrossRef] [EDP Sciences] [Google Scholar]
  36. W. Gangbo and A.R. Mészáros, Global well-posedness of master equations for deterministic displacement convex potential mean field games. Commun. Pure Appl. Math. to appear. Preprint available at https://arxiv.org/abs/2004.01660. [Google Scholar]
  37. W. Gangbo and A. Swiech, Existence of a solution to an equation arising in the theory of mean field games. J. Diff. Equ. 259 (2015) 6573–6643. [Google Scholar]
  38. D. Helbing, Quantitative Sociodynamics: Stochastic Methods and Models of Social Interaction Processes. Springer Science & Business Media (2010). [CrossRef] [Google Scholar]
  39. M.O. Jackson, Social and Economic Networks. Princeton University Press (2010). [CrossRef] [Google Scholar]
  40. S.N. Kružkov, First order quasilinear equations with several independent variables. Mat. Sb. (N.S.) 123 (1970) 228–255. [Google Scholar]
  41. H. Kunita, Stochastic Differential Equations and Stochastic Flows of Diffeomorphisms. Lecture Notes in Math. Springer-Verlag (1984). [Google Scholar]
  42. R.J. LeVeque, Finite Volume Methods for Hyperbolic Problems. Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge (2002). [Google Scholar]
  43. O.A. Manita, M.S. Romanov and S.V. Shaposhnikov, On uniqueness of solutions to nonlinear Fokker-Planck-Kolmogorov equations. Nonlinear Anal. 128 (2015) 199–226. [Google Scholar]
  44. O.A. Manita and S.V. Shaposhnikov, Nonlinear parabolic equations for measures. St. Petersburg Math. J. 25 (2014) 43–62. [Google Scholar]
  45. A. Muntean, J. Rademacher and A. Zagaris, Macroscopic and Large Scale Phenomena: Coarse Graining, Mean Field Limits and Ergodicity. Springer (2016). [CrossRef] [Google Scholar]
  46. B. Øksendal, Stochastic Differential Equations. Springer (2003). [CrossRef] [Google Scholar]
  47. S. Peng and Z. Wu, Fully coupled forward-backward stochastic differential equations and applications to optimal control. SIAM J. Control Optim. 37 (1999) 825–843. [Google Scholar]
  48. B. Piccoli and F. Rossi, Transport Equation with Nonlocal Velocity in Wasserstein spaces: convergence of numerical schemes. Acta App. Math. 124 (2013) 73–105. [Google Scholar]
  49. B. Piccoli, F. Rossi and E. Trélat, Control of the kinetic Cucker-Smale model. SIAM J. Math. Anal. 47 (2015) 4685–4719. [Google Scholar]
  50. N. Pogodaev, Optimal control of continuity equations. NoDEA 23 (2016) 21. [CrossRef] [Google Scholar]
  51. R. Sepulchre, Consensus on nonlinear spaces. Annu. Rev. Control 35 (2011) 56–64. [CrossRef] [Google Scholar]
  52. A.S. Sznitman, Topics in Propagation of Chaos. Springer-Verlag, Berlin (1991). [Google Scholar]
  53. T. Tao, An Epsilon of Room, I: Real Analysis: pages from year three of a mathematical blog. Vol. 117 of Graduate Studies in Mathematics. American Mathematical Society (2010). [CrossRef] [Google Scholar]
  54. C. Villani, Topics in Optimal Transportation. Vol. 58 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI (2003). [CrossRef] [Google Scholar]
  55. C. Villani, Optimal Transport: Old and New. Springer-Verlag, Berlin (2009). [CrossRef] [Google Scholar]

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