奇摄动方程的广义激波层解（英）

冯依虎, 莫嘉琪

doi:10.3969/j.issn.1005-3085.2018.01.010

工程数学学报 >

2018 , Vol. 35 >Issue 1: 101 - 109

DOI: https://doi.org/10.3969/j.issn.1005-3085.2018.01.010

奇摄动方程的广义激波层解（英）

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1- 亳州学院电子与信息工程系，亳州 236800
2- 安徽师范大学数学系，芜湖 241003

收稿日期: 2015-12-17

录用日期: 2016-05-10

网络出版日期: 2016-05-10

基金资助

国家自然科学基金(11202106)；安徽省教育厅自然科学基金(KJ2015A347)；安徽省高校优秀青年人才重点项目(gxyqZD2016520).

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The Generalized Shock Layer Solution to Singular Perturbation Equation

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1- Department of Electronics and Information Engineering, Bozhou College, Bozhou 236800
2- Department of Mathematics, Anhui Normal University, Wuhu 241003

Received date: 2015-12-17

Accepted date: 2016-05-10

Online published: 2016-05-10

Supported by

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 (gxyqZD2016520).

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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．

关键词： 奇异摄动问题; 反应扩散方程; 广义渐近解

本文引用格式

冯依虎, 莫嘉琪 . 奇摄动方程的广义激波层解（英）[J]. 工程数学学报, 2018 , 35(1) : 101 -109 . DOI: 10.3969/j.issn.1005-3085.2018.01.010

Abstract

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.

Key words： singular perturbation problem; reaction diffusion equation; generalized asymptotic solution

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