Convergence towards the population cross-diffusion system from stochastic many-particle system
Probability
2023-08-22 v2 Analysis of PDEs
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 Gronwall type estimate by using Taylor's expansion around the limiting stochastic process.
Cite
@article{arxiv.2301.03306,
title = {Convergence towards the population cross-diffusion system from stochastic many-particle system},
author = {Yue Li and Li Chen and Zhipeng Zhang},
journal= {arXiv preprint arXiv:2301.03306},
year = {2023}
}