两参数非线性反应-扩散系统的尖层冲击波解

doi:10.12341/jssms13062

系统科学与数学 ›› 2017, Vol. 37 ›› Issue (1): 304-312.DOI: 10.12341/jssms13062

两参数非线性反应-扩散系统的尖层冲击波解

欧阳成¹，林万涛²，莫嘉琪³

1. 湖州师范学院理学院, 湖州 313000;2. 中国科学院大气物理研究所, 大气科学和地球流体力学数值模拟国家重点实验室,北京 100029; 3. 安徽师范大学数学系, 芜湖 241003

出版日期:2017-01-25 发布日期:2017-03-31

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欧阳成，林万涛，莫嘉琪. 两参数非线性反应-扩散系统的尖层冲击波解[J]. 系统科学与数学, 2017, 37(1): 304-312.

OUYANG Cheng, LIN Wantao, MO Jiaqi. The Pointed Layer Shock Wave Solution of Reaction-Diffusion System with Two Parameters[J]. Journal of Systems Science and Mathematical Sciences, 2017, 37(1): 304-312.

The Pointed Layer Shock Wave Solution of Reaction-Diffusion System with Two Parameters

OUYANG Cheng¹, LIN Wantao², MO Jiaqi³

1. Faculty of Science, Huzhou University, Huzhou 313000; 2. State Key Laboratory of Numerical modeling for Atmospheric and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029; 3. Department of Mathematics, Anhui Normal University, Wuhu 241003

Online:2017-01-25 Published:2017-03-31

研究了一类两参数反应-扩散系统奇摄动Robin初始-边值问题. 首先,利用奇摄动方法, 联系到两个小参数构造了问题的外部解.其次,利用伸长变量分别得到了原问题解的的冲击波尖层, 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, 并利用微分不等式理论证明了渐近解的一致有效性.由本方法求原问题的渐近解, 它还可以进一步进行微分, 积分等解析运算, 从而能了解相应冲击波解的更深层的性态. 因此本方法具有良好的应用前景.

关键词： 反应-扩散系统, 尖层, 冲击波.

A class of nonlinear reaction diffusion singularly perturbed Robin initial-boundary problem with two parameters is studied. Firstly, using singular perturbation method, the outer solution for the problem is structured related two small parameters. Secondly, using the stretched variables, the pointed layer of shock wave solution, 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 differential inequality. Using this method 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 pointed layer of shock wave solution. Thus, this method possesses good applied foreground.

MR(2010)主题分类:

35B25

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[1]	莫嘉琪，林万涛，杜增吉. 具双参数非线性高阶椭圆型方程的奇摄动解[J]. 系统科学与数学, 2013, 33(2): 217-221.
[2]	莫嘉琪. 具有两参数的非线性椭圆型方程边值问题解的渐近性态[J]. 系统科学与数学, 2010, 30(9): 1185-1190.
[3]	陈怀军;莫嘉琪. 一类燃烧奇摄动问题的渐近估计[J]. 系统科学与数学, 2010, 30(1): 114-117.
[4]	刘树德;莫嘉琪. 双参数半线性高阶椭圆型方程的奇摄动解[J]. 系统科学与数学, 2009, 29(2): 168-173.
[5]	莫嘉琪. 椭圆型方程奇摄动问题的广义解[J]. 系统科学与数学, 2008, 28(3): 379-384.

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