一类奇摄动时滞反应扩散方程的空间对照结构

doi:10.3969/j.issn.1000-5641.2023.02.006

摘要/Abstract

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

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

中图分类号:

O175.26

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.

Qingzhao GAN, Mingkang NI. Contrast structure in a singularly perturbed delay reaction-diffusion equation[J]. Journal of East China Normal University(Natural Science), 2023, 2023(2): 34-47.

图/表 1

参考文献 35

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