Mean field limit with proliferation

Franco  Flandoli; Matti  Leimbach

doi:10.3934/dcdsb.2016086

Article Contents

2016, Volume 21, Issue 9: 3029-3052. Doi: 10.3934/dcdsb.2016086

This issue Previous Article An integral inequality for the invariant measure of some finite dimensional stochastic differential equation Next Article Well-posedness of stochastic primitive equations with multiplicative noise in three dimensions

Mean field limit with proliferation

Franco Flandoli^1, and
Matti Leimbach^2,

1.
Universita di Pisa, Dipartimento Matematica, Largo Bruno Pontecorvo 5, C.A.P. 56127, Pisa
2.
Technische Universität Berlin, Institut für Mathematik, Straße des 17. Juni 136, D-10623, Berlin

Received: September 30, 2015

Revised: February 29, 2016

Published: October 2016

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Abstract

An interacting particle system with long range interaction is considered. Particles, in addition to the interaction, proliferate with a rate depending on the empirical measure. We prove convergence of the empirical measure to the solution of a parabolic equation with non-local nonlinear transport term and proliferation term of logistic type.

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Mathematics Subject Classification: Primary: 60K35, 35K57; Secondary: 60F17, 35K58.

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