Abstract
Here, we establish the existence of weak solutions to a wide class of time-dependent monotone mean-field games (MFGs). These MFGs are given as a system of degenerate parabolic equations with initial and terminal conditions. To construct these solutions, we consider a high-order elliptic regularization in space–time. Then, applying Schaefer’s fixed-point theorem, we obtain the existence and uniqueness for this regularized problem. Using Minty’s method, we prove the existence of a weak solution to the original MFG. Finally, the paper ends with a discussion on congestion problems and density constrained MFGs.
Original language | English (US) |
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Pages (from-to) | 112470 |
Journal | Nonlinear Analysis |
Volume | 212 |
DOIs | |
State | Published - Jun 30 2021 |
ASJC Scopus subject areas
- Analysis
- Applied Mathematics