Existence of weak solutions to time-dependent mean-field games

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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 languageEnglish (US)
Pages (from-to)112470
JournalNonlinear Analysis
StatePublished - Jun 30 2021

Bibliographical note

KAUST Repository Item: Exported on 2021-07-02

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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