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

Autor: Vardan Voskanyan, Diogo A. Gomes
Rok vydání: 2015
Předmět:
Zdroj: Journal of the London Mathematical Society. 92:778-799
ISSN: 1469-7750
0024-6107
DOI: 10.1112/jlms/jdv052
Popis: We consider time-dependent mean-field games with congestion that are given by a system of a Hamilton-Jacobi equation coupled with a Fokker-Planck equation. The congestion effects make the Hamilton-Jacobi equation singular. These models are motivated by crowd dynamics where agents have difficulty moving in high-density areas. Uniqueness of classical solutions for this problem is well understood. However, existence of classical solutions, was only known in very special cases - stationary problems with quadratic Hamiltonians and some time-dependent explicit examples. Here, we prove short-time existence of $C^\infty$ solutions in the case of sub-quadratic Hamiltonians.
Databáze: OpenAIRE
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