| 高维Kramers系统离出点的分布问题 |
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| 引用本文： | 许金刚,包立平,吴立群.高维Kramers系统离出点的分布问题[J].应用数学与计算数学学报,2014,28(3):356-365. |
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| 作者姓名： | 许金刚 包立平 吴立群 |
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| 作者单位： | 1. 杭州电子科技大学理学院,杭州,310018
2. 杭州电子科技大学机械工程学院,杭州,310018 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 通过对高维Kramers系统与之对应稳态Fokker-Planck方程的渐近分析,仔细探讨了该系统在平衡点吸引域的边界上离出点的分布问题.运用变量替换、匹配原理、局部坐标变换、边界层展开等方法,对外解、远离鞍点处的边界层及鞍点处的边界层进行分析,得出离出点分布的渐近表达式.
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| 关 键 词： | 分布密度 渐近分析 离出分布 |
Exit distribution problem of high-dimension Kramers system |
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| XU Jin-gang,BAO Li-ping,WU Li-qun.Exit distribution problem of high-dimension Kramers system[J].Communication on Applied Mathematics and Computation,2014,28(3):356-365. |
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| Authors: | XU Jin-gang BAO Li-ping WU Li-qun |
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| Institution: | XU Jin-gang, BAO Li-ping, WU Li-qun (1. School of Science, Hangzhou Dianzi University, Hangzhou 310018, China; 2. School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China) |
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| Abstract: | The exit distribution problem of high dimension Kramers system on the boundary of the domain of attraction of the equilibrium is discussed through the asymptotic analysis of its corresponding stationary Fokker-Planck equation. The formulation of the exit distribution is obtained by the analysis of the outer solution and the boundary layer far from and near the saddle point. The asymptotic formulation of the exit distribution is obtained. |
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| Keywords: | probability density asymptotic analysis exit distribution |
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