华东师范大学学报（自然科学版） >

2023 , Vol. 2023 >Issue 2: 34 - 47

DOI: https://doi.org/10.3969/j.issn.1000-5641.2023.02.006

数学

一类奇摄动时滞反应扩散方程的空间对照结构

  • 甘清照 ,
  • 倪明康
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  • 华东师范大学 数学科学学院, 上海　200241

收稿日期: 2021-05-19

  网络出版日期: 2023-03-23

基金资助

国家自然科学基金(11471118); 上海市科学技术委员会基金(18dz2271000)

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Contrast structure in a singularly perturbed delay reaction-diffusion equation

  • Qingzhao GAN ,
  • Mingkang NI
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  • School of Mathematical Sciences, East China Normal University, Shanghai　200241, China

Received date: 2021-05-19

  Online published: 2023-03-23

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摘要

研究了一类具有非线性反应项的奇摄动时滞反应扩散方程的Neumann边值问题. 运用边界层函数法、空间对照结构理论和压缩映射原理构造该问题解的渐近展开式并证明了解的存在性. 最后给出一个具体的例子说明了结果的有效性.

关键词： 时滞; 反应扩散方程; 奇摄动; 角层; 空间对照结构; 渐近展开

本文引用格式

甘清照 , 倪明康 . 一类奇摄动时滞反应扩散方程的空间对照结构[J]. 华东师范大学学报（自然科学版）, 2023 , 2023(2) : 34 -47 . DOI: 10.3969/j.issn.1000-5641.2023.02.006

Abstract

This paper considers a Neumann boundary value problem of a singularly perturbed delay reaction-diffusion equation with a nonlinear reactive term. By using the boundary layer function method, contrast structure theory, and contraction mapping principle, the asymptotic expansion of the solution is constructed, and the existence of a uniformly valid solution is proven. Finally, an example is presented to show the effectiveness of our result.

Key words： delay; reaction-diffusion equation; singular perturbation; triangle layer; contrast structure; asymptotic expansion

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