| 韩祥临,莫嘉琪.两参数奇异摄动非线性双曲型微分系统的 过渡冲击层广义解[J].数学年刊A辑,2019,40(3):247~258 |
| 两参数奇异摄动非线性双曲型微分系统的 过渡冲击层广义解 |
| The Generalized Solution for Transitional Shock Layer to Singularly Perturbed Nonlinear Hyperbolic Type Differential System with Two Parameters |
| Received:April 02, 2018 Revised:October 06, 2018 |
| DOI：10.16205/j.cnki.cama.2019.0020 |
| 中文关键词: Differential system, Transitional layer, Small parameter |
| 英文关键词:Differential system, Transitional layer, Small parameter |
| 基金项目:本文受到国家自然科学基金(No.11771005)的资助. |
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| 中文摘要: |
| 研究了一类两参数双曲型微分系统奇异摄动初始边值问题. 首先,
利用奇异摄动理论和方法, 注意到两个小参数, 构造了问题的外部解.
其次, 利用多重尺度变量和伸长变量, 分别得到了原问题解的过渡冲击层、边界层和初始层校正项.
最后, 得到了原问题解的渐近展开式,
并利用泛函分析不动点理论, 证明了渐近解的一致有效性.
由本方法求得的原问题的渐近解, 它还可以进行微分, 积分等解析运算,
从而能了解相应过渡冲击层解的更进一步的性态.
因此本方法具有良好的应用前景. |
| 英文摘要: |
| A class of nonlinear hyperbolic type differential
system to singularly perturbed initial-boundary problem with two
parameters is studied. Firstly, using singular perturbation theory
and method, the outer solution for the problem is structured
related two small parameters. Secondly, using the multi-scale and
stretched variables, the transitional shock layer, boundary layer
and initial layer corrective terms are obtained for the original
problem respectively. Finally, the asymptotic expansion of solution
for the original problem is given. And the uniform validity of its
asymptotic solution is proved by using the theory of fixed point
of functional analysis. Using this method to obtained asymptotic
solution of original problem, it can also carry on analytical
operation for the differential and integral and so on. It is known
more behaviors for the transitional shock layer of solution. Thus
this method possesses good applied foreground. |
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