论文标题
抛物线抛物线凯勒 - 塞格模型的粒子近似值的平均场极限
Mean-field limit of a particle approximation for the parabolic-parabolic Keller-Segel model
论文作者
论文摘要
在本文中，我们通过建立从随机粒子系统到抛物线抛物性抛物性keller-segel-segel-segel-segel-segel（ks）方程的严格合并分析，研究了与对数截止的抛物线抛物性凯勒 - segel模型的混乱传播。假设初始数据是独立的，并且具有共同概率密度函数$ρ_0$的相同分布（i.i.d。），我们严格地证明了这种相互作用系统的混乱传播，其截止参数$ \ varepsilon \ varepsilon \ sim（\ ln n n）粒子系统的联合分布为$ f $ chaotic，尺寸$ f $具有密度，这是对平均场抛物线抛物线KS方程的弱解决方案。
In this paper, we study propagation of chaos for the parabolic-parabolic Keller-Segel model with a logarithmic cut-off by establishing a rigorous convergence analysis from a stochastic particle system to the parabolic-parabolic Keller-Segel (KS) equation for any dimension case. Under the assumption that the initial data are independent and identically distributed (i.i.d.) with a common probability density function $ρ_0$, we rigorously prove the propagation of chaos for this interacting system with a cut-off parameter $\varepsilon\sim (\ln N)^{-\frac{2}{d+2}}$: when $N\rightarrow \infty$, the joint distribution of the particle system is $f$-chaotic and the measure $f$ possesses a density which is a weak solution to the mean-field parabolic-parabolic KS equation.
