Swarming models with specular boundary condition and environmental noise
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908603211841536 |
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| author | Fetecau, Razvan C. Huang, Hui Qiu, Jinniao |
| author_facet | Fetecau, Razvan C. Huang, Hui Qiu, Jinniao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_02130 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Swarming models with specular boundary condition and environmental noise Fetecau, Razvan C. Huang, Hui Qiu, Jinniao Probability Analysis of PDEs Dynamical Systems 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. |
| title | Swarming models with specular boundary condition and environmental noise |
| topic | Probability Analysis of PDEs Dynamical Systems |
| url | https://arxiv.org/abs/2304.02130 |