KAUST DepartmentApplied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
KAUST Grant NumberOSR-CRG2017-3452
Online Publication Date2021-01-12
Print Publication Date2021-02
Embargo End Date2022-01-12
Permanent link to this recordhttp://hdl.handle.net/10754/662308
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AbstractIn 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.
CitationGomes, D. A., & Ribeiro, R. de L. (2021). Stationary mean-field games with logistic effects. SN Partial Differential Equations and Applications, 2(1). doi:10.1007/s42985-020-00053-9
SponsorsD. Gomes was partially supported by KAUST baseline funds and KAUST OSR-CRG2017-3452.