Mean field games with congestion
| Autor: | Alessio Porretta, Yves Achdou |
|---|---|
| Přispěvatelé: | Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Dipartimento di Matematica [Roma II] (DIPMAT), Università degli Studi di Roma Tor Vergata [Roma], ANR-16-CE40-0015,MFG,Jeux Champs Moyen(2016), ANR-12-MONU-0013,ISOTACE,Systemes d'Interactions, Transport Optimal, Applications a la simulation en Economie.(2012) |
| Rok vydání: | 2018 |
| Předmět: |
Mean field games
Congestion models Local coupling Existence and uniqueness Weak solutions Class (set theory) Type (model theory) 01 natural sciences symbols.namesake Mathematics - Analysis of PDEs Settore MAT/05 - Analisi Matematica FOS: Mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Applied mathematics Uniqueness 0101 mathematics Mathematical Physics Mathematics Partial differential equation Applied Mathematics 010102 general mathematics Zero (complex analysis) Optimal control 010101 applied mathematics Mean field theory symbols Hamiltonian (quantum mechanics) Analysis Analysis of PDEs (math.AP) |
| Zdroj: | Annales de l'Institut Henri Poincaré C, Analyse non linéaire. 35:443-480 |
| ISSN: | 1873-1430 0294-1449 |
| DOI: | 10.1016/j.anihpc.2017.06.001 |
| Popis: | We consider a class of systems of time dependent partial differential equations which arise in mean field type models with congestion. The systems couple a backward viscous Hamilton–Jacobi equation and a forward Kolmogorov equation both posed in ( 0 , T ) × ( R N / Z N ) . Because of congestion and by contrast with simpler cases, the latter system can never be seen as the optimality conditions of an optimal control problem driven by a partial differential equation. The Hamiltonian vanishes as the density tends to +∞ and may not even be defined in the regions where the density is zero. After giving a suitable definition of weak solutions, we prove the existence and uniqueness results of the latter under rather general assumptions. No restriction is made on the horizon T. |
| Databáze: | OpenAIRE |
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