SMOLUCHOWSKI-KRAMERS APPROXIMATION WITH STATE DEPENDENT DAMPING AND HIGHLY RANDOM OSCILLATION

被引：2

作者：

Lv, Yan ^{[1
]}

Wang, Wei ^{[2
]}

机构：

[1] Nanjing Univ Sci & Technol, Sch Math & Stat, Nanjing, Peoples R China

[2] Nanjing Univ, Dept Math, Nanjing, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2023年 / 28卷 / 01期

关键词：

Smoluchowski-Kramers approximation; stochastic differential equations; state dependent friction; random oscillation; martingale; WHITE-NOISE LIMITS; DIFFUSION-APPROXIMATION;

D O I：

10.3934/dcdsb.2022086

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The small mass limit (Smoluchowski-Kramers approximation) of class systems of ordinary differential equations describing motions of small mass particle with state dependent friction and high oscillation is derived by a diffusion approximation approach. In the small mass limit, due to the state dependent damping, one additional term appears in the limit equation, which leads to a stochastic differential equation (sDE) as the highly random oscillation appears as a multiplicative white noise.

引用

页码：499 / 515

页数：17