滞后微分方程在随机小扰动下惯性流形的逼近  

The approximation of inertial manifolds for retarded differential equation under small random perturbations

作　　者：陈美贤 申俊[1] CHEN Meixian;SHEN Jun(School of Mathematics,Sichuan University,Chengdu,Sichuan 610064,China)

机构地区：[1]四川大学数学学院,四川成都610064

出　　处：《内江师范学院学报》2024年第10期31-35,共5页Journal of Neijiang Normal University

基　　金：国家自然科学基金资助项目(11831012,12090010,12090013,12071317)。

摘　　要：考虑一类带着随机小扰动的滞后微分方程的惯性流形逼近问题.在适当条件下证明当小参数ε→0时,这类受加性白噪声驱动的随机滞后方程的惯性流形逐点收敛到对应的随机方程的惯性流形.The approximation of inertia manifolds for a class of retarded differential equations with stochastic small perturbations.Under appropriate conditions,it is proved that the inertial manifolds for this class of stochastic retarded eq uations driven by additive white noise converge pointwise to those of the corresponding random equations,as the small perturbationsε→0.

关 键 词：布朗运动 滞后微分方程 小扰动 惯性流形 收敛 

分 类 号：O175.12[理学—数学]