TY - JOUR

T1 - Short-time existence of solutions for mean-field games with congestion

AU - Gomes, Diogo A.

AU - Voskanyan, Vardan K.

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2015/11/20

Y1 - 2015/11/20

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/595341

UR - http://jlms.oxfordjournals.org/lookup/doi/10.1112/jlms/jdv052

UR - http://www.scopus.com/inward/record.url?scp=84950311543&partnerID=8YFLogxK

U2 - 10.1112/jlms/jdv052

DO - 10.1112/jlms/jdv052

M3 - Article

SN - 0024-6107

VL - 92

SP - 778

EP - 799

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

IS - 3

ER -