Brake orbits and heteroclinic connections for first order mean field games
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- by Annalisa Cesaroni and Marco Cirant PDF
- Trans. Amer. Math. Soc. 374 (2021), 5037-5070 Request permission
Abstract:
We consider first order variational mean field games (MFG) in the whole space, with aggregative interactions and density constraints, having stationary equilibria consisting of two disjoint compact sets of distributions with finite quadratic moments. Under general assumptions on the interaction potential, we provide a method for the construction of periodic in time solutions to the MFG, which oscillate between the two sets of static equilibria, for arbitrarily large periods. Moreover, as the period increases to infinity, we show that these periodic solutions converge, in a suitable sense, to heteroclinic connections. As a model example, we consider a MFG system where the interactions are of (aggregative) Riesz-type.References
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Additional Information
- Annalisa Cesaroni
- Affiliation: Dipartimento di Scienze Statistiche, Università di Padova, Via Battisti 241/243, 35121 Padova, Italy
- MR Author ID: 704474
- ORCID: 0000-0001-7159-8263
- Email: annalisa.cesaroni@unipd.it
- Marco Cirant
- Affiliation: Dipartimento di Matematica “Tullio Levi-Civita”, Università di Padova, Via Trieste 63, 35121 Padova, Italy
- MR Author ID: 1089238
- Email: cirant@math.unipd.it
- Received by editor(s): December 12, 2019
- Received by editor(s) in revised form: December 3, 2020
- Published electronically: April 20, 2021
- Additional Notes: The authors were partially supported by the Fondazione CaRiPaRo Project “Nonlinear Partial Differential Equations: Asymptotic Problems and Mean-Field Games”, and are members of GNAMPA-INdAM. The second author was partially supported by the Programme “FIL-Quota Incentivante” of University of Parma and co-sponsored by Fondazione Cariparma.
- © Copyright 2021 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 374 (2021), 5037-5070
- MSC (2020): Primary 49Q20, 35Q91
- DOI: https://doi.org/10.1090/tran/8362
- MathSciNet review: 4273184