Calculus of Variations and Geometric Measure Theory

M. Morandotti - F. Solombrino

Mean-field analysis of multi-population dynamics with label switching

created by morandott on 05 Jul 2019
modified by solombrin on 04 Apr 2020


Published Paper

Inserted: 5 jul 2019
Last Updated: 4 apr 2020

Journal: SIAM J. Math. Anal.
Volume: 52
Number: 2
Pages: 1427–1462
Year: 2020
Doi: 10.1137/19M1273426

ArXiv: 1907.02739 PDF


The mean-field analysis of a multi-population agent-based model is performed. The model couples a particle dynamics driven by a nonlocal velocity with a Markow-type jump process on the probability that each agent has of belonging to a given population. A general functional analytic framework for the well-posedness of the problem is established, and some concrete applications are presented, both in the case of discrete and continuous set of labels. In the particular case of a leader-follower dynamics, the existence and approximation results recently obtained in http:/cvgmt.sns.itpaper4137

are recovered and generalized as a byproduct of the abstract approach proposed.

Keywords: continuity equations, jump processes, superposition principle, kinetic equations, mean-field limits