| 欧阳成,莫嘉琪.两参数非线性反应扩散积分微分方程的内层激波渐近解[J].数学年刊A辑,2017,38(4):365~374 |
| 两参数非线性反应扩散积分微分方程的内层激波渐近解 |
| Interior Shock Asymptotic Solutions to Nonlinear Reaction Diffusion Integral Differential Equations with Two Parameters |
| Received:February 16, 2016 Revised:December 24, 2016 |
| DOI：10.16205/j.cnki.cama.2017.0030 |
| 中文关键词: Reaction diffusion, Singular perturbation, Initial boundary value problem |
| 英文关键词:Reaction diffusion, Singular perturbation, Initial boundary value problem |
| 基金项目:本文受到国家自然科学基金(No.11202106)和浙江省自然科学研究项目(No.LY13A010005)的资助. |
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| 中文摘要: |
| 研究了一类两参数非线性反应扩散积分微分奇摄动问题. 利用奇摄动方法,
构造了 问题的外部解、内部激波层、边界层及初始层校正项,
由此得到了问题解的形式渐近展开式. 最后利用积分微分
方程的比较定理证明了该问题解的渐近展开式的一致有效性. |
| 英文摘要: |
| The singular perturbation problem for the
nonlinear reaction diffusion integral differential problem with two
parameters is considered. By using the singular perturbation method,
the outer solution, interior shock layer, boundary layer and initial
layer corrective terms are constructed, then the formal asymptotic
expansion of solution is obtained. Finally, the uniform validity of
asymptotic expansion for solution to this problem is proved by using
the comparison theorem for integral differential equation. |
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