Swarming models with specular boundary condition and environmental noise

Razvan C. Fetecau; Hui Huang; Jinniao Qiu

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arXiv · 2304.02130

Swarming models with specular boundary condition and environmental noise

Razvan C. Fetecau·Hui Huang·Jinniao Qiu

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Abstract

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.

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BibTeX RIS

Razvan C. Fetecau, Hui Huang, Jinniao Qiu. 2023-04-04. Swarming models with specular boundary condition and environmental noise. https://arxiv.org/abs/2304.02130

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