• 论文 •

### 两参数非线性反应-扩散系统的尖层冲击波解

1. 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

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. 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

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.

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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.