Stationary mean-field games with logistic effects

Diogo A. Gomes, Ricardo de Lima Ribeiro

Research output: Contribution to journalArticlepeer-review

Abstract

In its standard form, a mean-field game is a system of a Hamilton-Jacobi equation coupled with a Fokker-Planck equation. In the context of population dynamics, it is natural to add to the Fokker-Planck equation features such as seeding, birth, and non-linear death rates. Here, we consider a logistic model for the birth and death of the agents. Our model applies to situations in which crowding increases the death rate. The new terms in this model require novel ideas to obtain the existence of a solution. Here, the main difficulty is the absence of monotonicity. Therefore, we construct a regularized model, establish a priori estimates for the solution, and then use a limiting argument to obtain the result.
Original languageEnglish (US)
JournalSN Partial Differential Equations and Applications
Volume2
Issue number1
DOIs
StatePublished - Jan 12 2021

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