华东师范大学学报(自然科学版) ›› 2026, Vol. 2026 ›› Issue (4): 1-12.doi: 10.3969/j.issn.1000-5641.2026.04.001

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一类奇摄动Burgers型方程的空间对照结构

吴潇(), 刘悦   

  1. 东华大学 数学与统计学院, 上海 201620
  • 收稿日期:2024-04-23 出版日期:2026-07-25 发布日期:2026-07-18
  • 作者简介:吴 潇, 男, 讲师, 研究方向为常微分方程与动力系统, 奇摄动理论和方法. E-mail: XiaoWu2022@dhu.edu.cn
  • 基金资助:
    中央高校基本科研业务费专项资金(2232023D-22)

Contrast structure in a singularly perturbed Burgers type equation

Xiao WU(), Yue LIU   

  1. School of Mathematics and Statistics, Donghua University, Shanghai 201620, China
  • Received:2024-04-23 Online:2026-07-25 Published:2026-07-18

摘要:

研究一类不连续奇异摄动Burgers型方程周期边值问题, 根据边界层函数法, 空间对照结构和微分不等式等方法, 证明空间对照结构型解的存在唯一性和局部稳定性, 并构造一致有效的渐近解.

关键词: 奇摄动Burgers型方程, 周期解, 内部层, 局部渐近稳定

Abstract:

This study considers the periodic boundary value problem for a class of singularly perturbed Burgers type equation with a discontinuous reaction term. Based on the boundary layer function method, contrast structure theory, and differential inequality methods, the existence and uniqueness as well as the local stability of the contrast structure solution are proved, and a high-precision asymptotic expansion of the solution is established.

Key words: singularly perturbed Burgers type equation, periodic solutions, internal layer, locally asymptotic stability

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