摘要
研究了一类广义奇摄动反应扩散方程初始边值问题.首先得到了原问题的外部解,然后利用广义函数理论构造了原问题的初始层和内部激波层项的广义渐近解.最后利用泛函分析不动点定理证明了具有广义激波层的渐近解的一致有效性.本文所用方法求得的激波渐近解具有简捷、有效和精度高的特点.
A class of generalized singular perturbation initial boundary value problem for the reaction diffusion equation is studied. Firstly, the outer solution to original problem is obtained. Next, the initial layer and interior shock layer corrective terms for the generalized asymptotic solutions to original problem are constructed by using the theory of generalized functions. Finally, used the fixed point theorem of functional analytic, the uniformly validity of the generalized asymptotic solution is proved.In this paper, the shock wave asymptotic solution possess simple, valid and higher accuracy peculiarity.
出处
《工程数学学报》
CSCD
北大核心
2018年第1期101-109,共9页
Chinese Journal of Engineering Mathematics
基金
The National Natural Science Foundation of China(11202106)
the Natural Science Foundation of the Education Department of Anhui Province(KJ2015A347)
the Key Projects of Outstanding Young Talents of Universities in Anhui Province(gxyq ZD2016520)
关键词
奇异摄动问题
反应扩散方程
广义渐近解
singular perturbation problem
reaction diffusion equation
generalized asymptotic solution
