Swarming models with specular boundary condition and environmental noise

We investigate a general class of models for swarming/self-collective behaviour in domains with boundaries. The model is expressed as a stochastic system of interacting particles subject to both reflecting boundary condition and common environmental noise. We rigorously derive its corresponding macr...

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Bibliographic Details
Main Authors Fetecau, Razvan C, Huang, Hui, Qiu, Jinniao
Format Journal Article
LanguageEnglish
Published 04.04.2023
Subjects
Mathematics - Analysis of PDEs
Mathematics - Dynamical Systems
Mathematics - Probability
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DOI10.48550/arxiv.2304.02130

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Summary:We investigate a general class of models for swarming/self-collective behaviour in domains with boundaries. The model is expressed as a stochastic system of interacting particles subject to both reflecting boundary condition and common environmental noise. We rigorously derive its corresponding macroscopic mean-field equation, which is a new type of stochastic partial differential equation due to the presence of common noise. The approach relies on a compactness argument, in which we first establish the tightness of the empirical measures associated with the particle system and then demonstrate that the time marginal of the limit measure is a solution to the mean-field equation.
DOI:10.48550/arxiv.2304.02130