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- W3174403913 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." @default.
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- W3174403913 date "2021-11-01" @default.
- W3174403913 modified "2023-09-29" @default.
- W3174403913 title "Existence of weak solutions to time-dependent mean-field games" @default.
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- W3174403913 doi "https://doi.org/10.1016/j.na.2021.112470" @default.
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