Short-time existence of solutions for mean-field games with congestion

Diogo A. Gomes, Vardan K. Voskanyan

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


We consider time-dependent mean-field games with congestion that are given by a Hamilton–Jacobi equation coupled with a Fokker–Planck equation. These models are motivated by crowd dynamics in which agents have difficulty moving in high-density areas. The congestion effects make the Hamilton–Jacobi equation singular. The uniqueness of solutions for this problem is well understood; however, the existence of classical solutions was only known in very special cases, stationary problems with quadratic Hamiltonians and some time-dependent explicit examples. Here, we demonstrate the short-time existence of C∞ solutions for sub-quadratic Hamiltonians.
Original languageEnglish (US)
Pages (from-to)778-799
Number of pages22
JournalJournal of the London Mathematical Society
Issue number3
StatePublished - Nov 20 2015


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