扩散粒子对FKPP方程的一致收敛性
Uniform convergence of proliferating particles to the FKPP equation
摘要：
本文考虑了一类扩散率依赖于经验测度的布朗粒子系统。这种依赖性比平均场的依赖性更局部，Oelschlager [17]，[18]称之为适度相互作用。我们证明了经验过程在空间变量上一致收敛于Fisher-Kolmogorov-Petrowskiii-Piskunov方程的解。我们使用的半群方法，这是新的框架，这些系统的启发，随机偏微分方程的一些文献。
英文摘要：
In this paper we consider a system of Brownian particles with proliferation whose rate depends on the empirical measure. The dependence is more local than a mean field one and has been called moderate interaction by Oelschlager [17], [18]. We prove that the empirical process converges, uniformly in the space variable, to the solution of the Fisher-Kolmogorov-Petrowskii-Piskunov equation. We use a semigroup approach which is new in the framework of these systems and is inspired by some literature on stochastic partial differential equations.
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