## 留言板

 引用本文: 包立平, 胡玉博, 吴立群. 具有初值间断的Burgers方程奇摄动解[J]. 应用数学和力学, 2020, 41(7): 807-816.
BAO Liping, HU Yubo, WU Liqun. Singularly Perturbed Solutions of Burgers Equations With Initial Value Discontinuities[J]. Applied Mathematics and Mechanics, 2020, 41(7): 807-816. doi: 10.21656/1000-0887.400270
 Citation: BAO Liping, HU Yubo, WU Liqun. Singularly Perturbed Solutions of Burgers Equations With Initial Value Discontinuities[J]. Applied Mathematics and Mechanics, 2020, 41(7): 807-816.

## 具有初值间断的Burgers方程奇摄动解

##### doi: 10.21656/1000-0887.400270

###### 作者简介:包立平(1962—)，男，副教授，博士(E-mail: baolp@hdu.edu.cn)；胡玉博(1992—)，女，硕士生(通讯作者. E-mail: 1195595626@qq.com).
• 中图分类号: O175.29

## Singularly Perturbed Solutions of Burgers Equations With Initial Value Discontinuities

Funds: The National Natural Science Foundation of China(51775154)
• 摘要: 讨论激光等离子体产生的波模型，形成了具有初值间断的Burgers方程Riemann问题，通过奇摄动展开的方法得到了具有间断初值的Burgers方程相应形式的奇摄动渐近解，渐近解包含外解和内部层矫正两部分.由于初值条件是常数，波在传播的过程中产生特征边界，矫正项为抛物边界即抛物型特征边界.对外解在特征边界上进行内部层矫正，利用HopfCole变换、Fourier变换、极值原理证明了渐近解的存在性、唯一性，得到了形式渐近展开式.证明了形式渐近解的一致有效性.
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##### 出版历程
• 收稿日期:  2019-09-12
• 修回日期:  2019-11-04
• 刊出日期:  2020-07-01

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