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一维弱噪声随机Burgers方程的奇摄动解

包立平 洪文珍

包立平, 洪文珍. 一维弱噪声随机Burgers方程的奇摄动解[J]. 应用数学和力学, 2018, 39(1): 113-122. doi: 10.21656/1000-0887.380068
引用本文: 包立平, 洪文珍. 一维弱噪声随机Burgers方程的奇摄动解[J]. 应用数学和力学, 2018, 39(1): 113-122. doi: 10.21656/1000-0887.380068
BAO Liping, HONG Wenzhen. Singular Perturbation Solutions to 1D Stochastic Burgers Equations Under Weak Noises[J]. Applied Mathematics and Mechanics, 2018, 39(1): 113-122. doi: 10.21656/1000-0887.380068
Citation: BAO Liping, HONG Wenzhen. Singular Perturbation Solutions to 1D Stochastic Burgers Equations Under Weak Noises[J]. Applied Mathematics and Mechanics, 2018, 39(1): 113-122. doi: 10.21656/1000-0887.380068

一维弱噪声随机Burgers方程的奇摄动解

doi: 10.21656/1000-0887.380068
基金项目: 国家自然科学基金(51175134)
详细信息
    作者简介:

    包立平(1962—),男,副教授,博士(通讯作者. E-mail: baolp@hdu.edu.cn);洪文珍(1991—),女,硕士生.

  • 中图分类号: O175.26|O211.63

Singular Perturbation Solutions to 1D Stochastic Burgers Equations Under Weak Noises

Funds: The National Natural Science Foundation of China(51175134)
  • 摘要: 讨论了一类有界区域上具有有色噪声干扰的随机Burgers方程奇摄动解,其波动率服从弱噪声Ornstein-Uhlenbeck(OU)过程由波运动的转移概率密度函数满足的后向Kolmogorov方程,得到随机Burgers的期望所满足的后向Kolmogorov方程由于期望满足的后向Kolmogorov方程的初边值问题条件涉及到一类确定性Burgers方程的解,因此该问题实际上是Burgers方程和Kolmogorov方程的联立形式首先,应用奇摄动方法,对一类确定性Burgers方程进行了正则渐近展开,由Schauder估计、Ascoli-Arzela 定理证明了非线性抛物方程渐近解的有界性与存在性,由Lax-Milgram定理证明了线性抛物方程渐近解的有界性与存在性,得到波速率的形式渐近解其次,由奇摄动理论,对期望满足的方程进行了奇摄动渐近展开和边界层矫正,由二阶线性偏微分方程理论,得到边界层函数渐近解存在且有界应用极值原理、De-Giorgi迭代技术分别证明了波速率和波期望渐近解的余项有界,得到渐近解的一致有效性.
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出版历程
  • 收稿日期:  2017-03-24
  • 修回日期:  2017-06-11
  • 刊出日期:  2018-01-15

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