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

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Propagation of Chaos
Particle System
Chaos theory
Aggregation
Sensing
Agglomeration
Boundary conditions
Fluxes
Convergence in Law
kernel
Mean Field Equation
Empirical Measures
Interacting Particle Systems
Collective Behavior
Continuity Equation
Stochastic Systems
Probability Measure
Weak Solution
Lipschitz
Infinity

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Applied Mathematics

Cite this

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Propagation of chaos for aggregation equations with no-flux boundary conditions and sharp sensing zones. / Choi, Young Pil; Salem, Samir.

In: Mathematical Models and Methods in Applied Sciences, Vol. 28, No. 2, 01.02.2018, p. 223-258.

Research output: Contribution to journalArticle

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