华东师范大学学报（自然科学版） ›› 2022, Vol. 2022 ›› Issue (1): 1-9.doi: 10.3969/j.issn.1000-5641.2022.01.001

• 数学 •    下一篇

一类右端不连续的奇摄动二阶半线性微分方程解的稳定性态

刘乐思(), 倪明康*()   

  1. 1. 华东师范大学 数学科学学院, 上海　200241
  • 收稿日期:2021-01-18 出版日期:2022-01-25 发布日期:2022-01-18
  • 通讯作者: 倪明康 E-mail:la1992@mail.ru;xiaovikdo@163.com
  • 基金资助:
    the National Nature Science Foundation of China (No.11871217) and the Science and Technology Commission of Shanghai Municipality (No.18dz2271000)

Stability of the solution to a singularly perturbed semilinear second-order differential equation with discontinuous right-hand side

Aleksei LIUBAVIN(), Mingkang NI*()   

  1. 1. School of Mathematical Sciences, East China Normal University, Shanghai　200241, China
  • Received:2021-01-18 Online:2022-01-25 Published:2022-01-18
  • Contact: Mingkang NI E-mail:la1992@mail.ru;xiaovikdo@163.com

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摘要：

本文研究了一类右端不连续的反应扩散方程的稳态问题. 基于空间对照结构理论, 通过求解Sturm-Liouville问题构造了特征值和特征函数的渐近展开式, 并给出了该表达式的余项估计以及稳态解稳定的充分性条件.

关键词: 奇摄动, 渐近逼近, 稳定性, 反应扩散方程

Abstract:

In this paper, a stationary problem for the reaction-diffusion equation with a discontinuous right-hand side is considered. Based on ideas from contrast structure theory, the asymptotic representations for eigenvalues and eigenfunctions are constructed by solving a Sturm-Liouville problem and an estimation of the remainder is obtained. Moreover, a sufficient condition which guarantees the stability of the solution to this task is established.

Key words: singular perturbations, asymptotic approximations, stability, reaction-diffusion equation

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