Stationary mean-field games with logistic effects

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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
Issue number1
StatePublished - Jan 12 2021

Bibliographical note

KAUST Repository Item: Exported on 2021-02-25
Acknowledged KAUST grant number(s): OSR-CRG2017-3452
Acknowledgements: D. Gomes was partially supported by KAUST baseline funds and KAUST OSR-CRG2017-3452.


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