Weak KAM approach to first-order Mean Field Games with state constraints
Cannarsa, Piermarco; Cheng, Wei; Mendico, Cristian; Wang, Kaizhi (2021), Weak KAM approach to first-order Mean Field Games with state constraints, Journal of Dynamics and Differential Equations, p. 33. 10.1007/s10884-021-10071-9
TypeArticle accepté pour publication ou publié
Journal nameJournal of Dynamics and Differential Equations
MetadataShow full item record
Dipartimento di Matematica [Roma II] [DIPMAT]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)We study the asymptotic behavior of solutions to the constrained MFG system as the time horizon T goes to infinity. For this purpose, we analyze first Hamilton-Jacobi equations with state constraints from the viewpoint of weak KAM theory, constructing a Mather measure for the associated variational problem. Using these results, we show that a solution to the constrained ergodic mean field games system exists and the ergodic constant is unique. Finally, we prove that any solution of the first-order constrained MFG problem on [0,T] converges to the solution of the ergodic system as T→+∞.
Subjects / KeywordsWeak KAM theory; Mean Field Games; State constraints; Semiconcave functions; Long-time behavior of solutions
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Cannarsa, Piermarco; Capuani, Rossana; Cardaliaguet, Pierre (2021) Article accepté pour publication ou publié