Year: 2024
Author: Yue Li, Li Chen, Zhipeng Zhang
Communications in Mathematical Research , Vol. 40 (2024), Iss. 1 : pp. 43–63
Abstract
In this paper, we derive rigorously a non-local cross-diffusion system from an interacting stochastic many-particle system in the whole space. The convergence is proved in the sense of probability by introducing an intermediate particle system with a mollified interaction potential, where the mollification is of algebraic scaling. The main idea of the proof is to study the time evolution of a stopped process and obtain a Grönwall type estimate by using Taylor’s expansion around the limiting stochastic process.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2023-0002
Communications in Mathematical Research , Vol. 40 (2024), Iss. 1 : pp. 43–63
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Stochastic particle systems cross-diffusion system mean-field limit population dynamics.