对流-扩散方程初边值问题的重整化群方法  

Renormalization Group Method for Initial-Boundary Value Problem of Convection-Diffusion Equation

作　　者：周冉[1] 张艳妮 ZHOU Ran;ZHANG Yanni(College of Mathematics,Jilin University,Changchun 130012,China;Department of Basic Science,Jilin University of Architecture and Technology,Changchun 130114,China)

机构地区：[1]吉林大学数学学院,长春130012 [2]吉林建筑科技学院基础科学部,长春130114

出　　处：《吉林大学学报（理学版）》2020年第5期1154-1158,共5页Journal of Jilin University:Science Edition

基　　金：吉林省教育厅科学研究规划项目(批准号:JJKH20200934KJ);吉林省科技厅面上项目(批准号:20190201132JC).

摘　　要：利用摄动重整化群方法研究一类对流-扩散方程的奇异摄动初边值问题.首先将时滞微分方程分解为左、右两个不带时滞的边值问题,然后利用重整化群方法分别构造左问题和右问题的渐近解,最后利用光滑缝接条件将左右两段解相连,得到原问题的逼近解.We studied a class of singular perturbation initial-boundary value problem of the convection-diffusion equation by using the perturbed renormalization group method.Firstly,the delay differential equation was decomposed into left and right boundary value problems without delay.Secondly,the asymptotic solutions of left and right problems were constructed by using renormalization group method.Finally,the left and right solutions were connected by smooth joint condition,and the asymptotic solutions of the original problem were obtained.

关 键 词：重整化群方法 奇异摄动 对流-扩散方程 

分 类 号：O175.12[理学—数学]