Mean field limit of a dynamical model of polymer systems

作     者：E Weinan SHEN Hao 

作者机构：School of Mathematical Sciences and BICMR Peking University Department of Mathematics and PACM Princeton UniversityPrinceton NJ 08544 USA Program in Applied and Computational Mathematics Princeton UniversityPrinceton NJ 08544 USA 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2013年第56卷第12期

页      面：2591-2598页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China(Grant No.91130005) the US Army Research Office(Grant No.W911NF-11-1-0101) 

主　　题：polymers mean field limit stochastic PDEs McKean-Vlasov equation 

摘      要：This paper provides a mathematically rigorous foundation for self-consistent mean field theory of the polymeric physics. We study a new model for dynamics of mono-polymer systems. Every polymer is regarded as a string of points which are moving randomly as Brownian motions and under elastic forces. Every two points on the same string or on two different strings also interact under a pairwise potential V. The dynamics of the system is described by a system of N coupled stochastic partial differential equations （SPDEs）. We show that the mean field limit as N -＋ c~ of the system is a self-consistent McKean-Vlasov type equation, under suitable assumptions on the initial and boundary conditions and regularity of V. We also prove that both the SPDE system of the polymers and the mean field limit equation are well-posed.