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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 ›› 2021, Vol. 38 ›› Issue (4): 564-572.doi: 10.3969/j.issn.1005-3085.2021.04.010

• • 上一篇    下一篇

非线性奇摄动积分-微分发展方程Robin问题广义解

冯依虎1,2,   莫嘉琪3   

  1. 1- 亳州学院电子与信息工程系，亳州  236800 2- 上海大学数学系，上海  200436 3- 安徽师范大学数学与统计学院，芜湖  241003
  • 收稿日期:2019-04-08 接受日期:2020-03-06 出版日期:2021-08-15 发布日期:2021-10-15
  • 基金资助:
    国家自然科学基金 (41275062)；安徽省教育厅自然科学重点基金 (KJ2017A90; KJ2018A0964)；安徽省高校优秀青年人才支持计划重点项目 (gxyqZD2016520)；安徽省高等学校省级质量工程重点教研项目 (2018jyxm0594).

The Generalized Solution for the Nonlinear Singular Perturbation Robin Problem of Integral-differential Evolution Equation

FENG Yi-hu1,2,   MO Jia-qi3   

  1. 1- Department of Electronics and Information Engineering, Bozhou College, Bozhou 236800
    2- Department of Mathematics, Shanghai University, Shanghai 200436
    3- School of Mathematics & Statistics, Anhui Normal University, Wuhu 241003
  • Received:2019-04-08 Accepted:2020-03-06 Online:2021-08-15 Published:2021-10-15
  • Supported by:
    The National Natural Science Foundation of China (41275062); the Natural Science Foundation of the Education Department of Anhui Province (KJ2017A90; KJ2018A0964); the Key Projects of Outstanding Young Talents of Universities in Anhui Province (gxyqZD2016520); the Key Teaching Project of Anhui Provincial Quality Projects of Colleges and Universities (2018jyxm0594).

PDF (PC)

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摘要： 讨论了一类广义非线性奇异摄动积分-微分发展方程Robin问题．首先，利用广义Fredholm积分方程求解方法，得到了模型的外部解．其次，引入多重尺度变量，构造了Robin问题解的边界层校正项．然后利用伸长变量，得到了解的初始层校正项，并构造了奇异摄动问题的形式解的合成展开式．最后，用泛函分析不动点理论证明了广义解的渐近展开式的一致有效性．

关键词: 奇摄动, 发展方程, 渐近解

Abstract: A class of generalised nonlinear singular perturbation integral-differential evolution equation Robin problem is discussed. Firstly, the outer solution of the model is obtained by using a solving method of the Fredholm type integral equation. Next, the boundary layer corrective term of the solution is constructed by using the variables of multiple scales. Then the initial layer corrective term of the solution for the original model is found using the stretched variable. And the composed expansion of formal solution for the singular perturbation problem is constructed. Finely, the asymptotic expansion of the generalised solution is proved by using the fixed point theory of the functional analysis.

Key words: singular perturbation, evolution equation, asymptotic solution

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