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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (2): 291-297.doi: 10.3969/j.issn.1005-3085.2015.02.013

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具有边界摄动的反应扩散时滞方程奇摄动问题(英)

汪维刚1,   石兰芳2,   韩祥临3,   莫嘉琪4   

  1. 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
  • 收稿日期:2013-06-25 接受日期:2014-12-26 出版日期:2015-04-15 发布日期:2015-06-15
  • 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 (KJ2013A133)；江苏省高校自然科学基金 (13KJB170016)；浙江省自然科学基金 (LY13A010005).

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

WANG Wei-gang1,   SHI Lan-fang2,   HAN Xiang-lin3,   MO Jia-qi4   

  1. 1- Department of Science and Technology, Tongcheng Teachers College, Tongcheng, Anhui 231400
    2- College of Mathematics and Statistics, Nanjing University of Information Science & Technology, Nanjing, Jiangsu 210044
    3- School of Science, Huzhou University, Huzhou, Zhejiang 313000
    4- Department of Mathematic, Anhui Normal University, Wuhu, Anhui 241003
  • Received:2013-06-25 Accepted:2014-12-26 Online:2015-04-15 Published:2015-06-15
  • Supported by:
    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). 

PDF (PC)

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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．

关键词: 非线性, 反应扩散, 奇摄动

Abstract:

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.

Key words: nonlinear, reaction diffusion, singular perturbation

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