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 . 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.
@article{AIHPC_2018__35_2_443_0,
author = {Achdou, Yves and Porretta, Alessio},
title = {Mean field games with congestion},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {443--480},
year = {2018},
publisher = {Elsevier},
volume = {35},
number = {2},
doi = {10.1016/j.anihpc.2017.06.001},
mrnumber = {3765549},
zbl = {1476.35100},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2017.06.001/}
}
TY - JOUR AU - Achdou, Yves AU - Porretta, Alessio TI - Mean field games with congestion JO - Annales de l'I.H.P. Analyse non linéaire PY - 2018 SP - 443 EP - 480 VL - 35 IS - 2 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2017.06.001/ DO - 10.1016/j.anihpc.2017.06.001 LA - en ID - AIHPC_2018__35_2_443_0 ER -
%0 Journal Article %A Achdou, Yves %A Porretta, Alessio %T Mean field games with congestion %J Annales de l'I.H.P. Analyse non linéaire %D 2018 %P 443-480 %V 35 %N 2 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2017.06.001/ %R 10.1016/j.anihpc.2017.06.001 %G en %F AIHPC_2018__35_2_443_0
Achdou, Yves; Porretta, Alessio. Mean field games with congestion. Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 2, pp. 443-480. doi: 10.1016/j.anihpc.2017.06.001
Cité par Sources :