Rigorous mean-field limit and cross-diffusion
Rigorous mean-field limit and cross-diffusion
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DOI：
10.1007/s00033-019-1170-7
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发表时间：
2018-10
期刊：
影响因子：
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通讯作者：
Li Chen;Esther S. Daus;A. Jüngel
中科院分区：
文献类型：
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作者：
Li Chen;Esther S. Daus;A. Jüngel
证明了多种群弱相互作用随机多粒子系统在全空间的平均场极限。限制系统由交叉扩散方程组成，模拟种群的分离。平均场极限分两步实现：首先，多粒子系统引入大粒子数极限，得到一个中间非局域扩散系统。当相互作用势接近Dirac δ分布时，由非局部系统得到局部交叉扩散系统，证明了小初值条件下极限扩散系统和中间扩散系统的整体存在性，并给出了误差估计.
The mean-field limit in a weakly interacting stochastic many-particle system for multiple population species in the whole space is proved. The limiting system consists of cross-diffusion equations, modeling the segregation of populations. The mean-field limit is performed in two steps: First, the many-particle system leads in the large population limit to an intermediate nonlocal diffusion system. The local cross-diffusion system is then obtained from the nonlocal system when the interaction potentials approach the Dirac delta distribution.The global existence of the limiting and the intermediate diffusion systems is shown for small initial data, and an error estimate is given.