On mean field systems with multi-classes

Dung Tien Nguyen; Son Luu Nguyen; Nguyen Huu Du

doi:10.3934/dcds.2020057

Article Contents

2020, Volume 40, Issue 2: 683-707. Doi: 10.3934/dcds.2020057

This issue Previous Article Next Article Global existence for semilinear damped wave equations in relation with the Strauss conjecture

On mean field systems with multi-classes

1.
Department of Applied Mathematics, Faculty of Applied Science, Ho Chi Minh City University of Technology, Vietnam National University Ho Chi Minh City, 268 Ly Thuong Kiet, District 10, Ho Chi Minh City, Vietnam
2.
Department of Mathematics, University of Puerto Rico, Rio Piedras campus, San Juan, PR 00925, Puerto Rico
3.
Department of Mathematics, Mechanics and Informatics, Hanoi National University, 334 Nguyen Trai, Thanh Xuan, Hanoi Vietnam

^* Corresponding author: Dung Tien Nguyen
^* Corresponding author: Dung Tien Nguyen

Received: April 30, 2018

Revised: July 31, 2019

Published: November 2019

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Abstract

This work focuses on stochastic systems of weakly interacting particles containing different populations represented by multi-classes. The dynamics of each particle depends not only on the empirical measure of the whole population but also on those of different populations. The limits of such systems as the number of particles tends to infinity are investigated. We establish the existence, uniqueness, and basic properties of solutions to the limiting McKean-Vlasov equations of these systems and then obtain the rate of convergence of the sequences of empirical measures associated with the systems to their limits in terms of the $ p^{\text{th}} $ Monge-Wasserstein distance.

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Mathematics Subject Classification: Primary: 60F25, 93E03; Secondary: 60J60.

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