Propagation of chaos for aggregation equations with no-flux boundary conditions and sharp sensing zones

Young Pil Choi, Samir Salem

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We consider an interacting N-particle system with the vision geometrical constraints and reflected noises, proposed as a model for collective behavior of individuals. We rigorously derive a continuity-type of mean-field equation with discontinuous kernels and the normal reflecting boundary conditions from that stochastic particle system as the number of particles N goes to infinity. More precisely, we provide a quantitative estimate of the convergence in law of the empirical measure associated to the particle system to a probability measure which possesses a density which is a weak solution to the continuity equation. This extends previous results on an interacting particle system with bounded and Lipschitz continuous drift terms and normal reflecting boundary conditions by Sznitman [J. Funct. Anal. 56 (1984) 311-336] to that one with discontinuous kernels.

Original languageEnglish
Pages (from-to)223-258
Number of pages36
JournalMathematical Models and Methods in Applied Sciences
Volume28
Issue number2
DOIs
Publication statusPublished - 2018 Feb 1

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Applied Mathematics

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