非线性奇摄动问题的广义内部冲击层解

doi:10.3969/j.issn.0253-2778.2015.08.004

中国科学技术大学学报 ›› 2015, Vol. 45 ›› Issue (8): 638-642.DOI: 10.3969/j.issn.0253-2778.2015.08.004

非线性奇摄动问题的广义内部冲击层解

陈怀军

1.安徽师范大学数学系，安徽芜湖 241003;2.南京信息工程大学数学与统计学院，江苏南京 210044

收稿日期:2015-04-14 修回日期:2015-07-02 出版日期:2015-08-31 发布日期:2015-08-31
作者简介:CHEN Huaijun, female, born in 1964, master/ associate Prof. Research field: applied mathematics.

A generalized interior shock layer solution to nonlinear singularly perturbed equations

CHEN Huaijun

1.Department of Mathematics, Anhui Normal University, Wuhu 241003，China; 2.College of Mathematics and Statistics, Nanjing University of Information Science & Technology, Nanjing 210044, China

Received:2015-04-14 Revised:2015-07-02 Online:2015-08-31 Published:2015-08-31
Contact: MO Jiaqi

摘要/Abstract

摘要： 研究了一类广义奇摄动反应扩散方程初始边值问题. 在适当的假设下, 考虑了退化问题的广义解，然后利用广义函数理论构造了原问题的冲击层和边界层渐近解.再利用不动点定理证明了具有广义内部冲击层的渐近解的一致有效性.

关键词: 奇摄动, 非线性方程, 冲击层

Abstract: A class of singular perturbation problem of the reaction diffusion initial value equation was studied. Under suitable conditions, the generalized outer solution to reduced problems was considered. Then the interior shock and boundary layer correction solutions to the original problem were constructed by using the theory of generalized functions. Finally, using the fixed point theorem, the uniform validity of the generalized asymptotic solution with interior shock and initial layers was proved.

Key words: singular perturbation, nonlinear equation, shock layer

陈怀军，石兰芳，莫嘉琪. 非线性奇摄动问题的广义内部冲击层解[J]. 中国科学技术大学学报, 2015, 45(8): 638-642.

CHEN Huaijun, SHI Lanfang, MO Jiaqi. A generalized interior shock layer solution to nonlinear singularly perturbed equations[J]. Journal of University of Science and Technology of China, 2015, 45(8): 638-642.

[1]	朱红宝，陈松林，杜亚洁. 一类非线性时滞奇异摄动边值问题的激波解[J]. 中国科学技术大学学报, 2020, 50(2): 115-119.
[2]	朱红宝. 一类非线性奇摄动时滞边值问题的激波解[J]. 中国科学技术大学学报, 2018, 48(5): 357-360.

非线性奇摄动问题的广义内部冲击层解

A generalized interior shock layer solution to nonlinear singularly perturbed equations

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 2

编辑推荐

Metrics

本文评价