具有边界摄动的反应扩散时滞方程奇摄动问题(英文)  

Singular Perturbation Problem for Reaction Diffusion Time Delay Equation with Boundary Perturbation

作　　者：汪维刚 石兰芳[2] 韩祥临[3] 莫嘉琪[4] 

机构地区：[1]桐城师范高等专科学校理工系,安徽桐城231400 [2]南京信息工程大学数学与统计学院,江苏南京210044 [3]湖州师范学院理学院,浙江湖州313000 [4]安徽师范大学数学系,安徽芜湖241003

出　　处：《工程数学学报》2015年第2期291-297,共7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(KJ2013A133);the Natural Sciences Fundation from the Universities of Jiangsu Province(13KJB170016);the Natural Science Foundation of Zhejiang Province(LY13A010005)

摘　　要：本文研究了具有边界摄动的非线性时滞反应扩散方程奇摄动问题.首先得到了退化问题的解.其次构造了原问题的外部解.然后引入伸长变量构造了解的初始层校正项,得到了解的形式渐近展开式.最后在适当的假设下,利用微分不等式理论,证明了原初始边植问题解的渐近展开式的一致有效性.The nonlinear singular perturbation problem for the reaction diffusion time delay equation with boundary perturbation is considered in this paper. Firstly, the redu-ced solution is obtained. Secondly, the outer solution of the original problem is constructed. Then, introducing a stretched variable, the initial layer correction of solution is obtained. Finally, under the suitable conditions, applying the theory of differential inequalities the uniformly valid asymptotic expansion of solution for the original initial boundary value problem is proved.

关 键 词：非线性 反应扩散 奇摄动 

分 类 号：O175.29[理学—数学]