Calculus of Variations and Geometric Measure Theory

S. Almi - C. D'Eramo - M. Morandotti - F. Solombrino

Mean-field limits for entropic multi-population dynamical systems

created by morandott on 30 Sep 2022
modified by solombrino on 24 Apr 2023


Published Paper

Inserted: 30 sep 2022
Last Updated: 24 apr 2023

Journal: Milan Journal of Mathematics
Pages: 38
Year: 2023
Doi: 10.1007/s00032-022-00375-w


The well-posedness of a multi-population dynamical system with an entropy regularization and its convergence to a suitable mean-field approximation are proved, under a general set of assumptions. Under further assumptions on the evolution of the labels, the case of different time scales between the agents' locations and labels dynamics is considered. The limit system couples a mean-field-type evolution in the space of positions and an instantaneous optimization of the payoff functional in the space of labels.

Keywords: Entropic regularization, superposition principle, population dynamics, mean-field limit, fast reaction limit, replicator-type dynamics