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

2016/10/11 by Young-Pil Choi, Choi, Young-Pil, Samir Salem +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #Analysis of PDEs (math.AP) #Diffusion and Search Dynamics #FOS: Mathematics #Mathematical Biology Tumor Growth #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1610.03261

openalex publication_date 2016/10/11 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

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

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