Scholarlink

Abstract <p>For a singularly perturbed reaction–diffusion equation with periodic coefficients, the structure of the inner transition layer in the case of a balanced reaction with a weak discontinuity is investigated. The existence of periodic solutions with an inner transition layers is proven, their stability is analyzed, and asymptotic approximations of solutions of this type are obtained. It is demonstrated that in the case of reaction balance, the presence of even a weak (asymptotically small) reaction discontinuity can lead to the formation of several periodic contrast structures of finite size, both stable and unstable.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Periodic Inner Transition Layers in the Reaction–Diffusion Problem in the Case of Weak Reaction Discontinuity

  • 期刊论文

  • 发表日期：

    2025年2月1日

查看全文
  • E. I. Nikulin,
  • V. T. Volkov,
  • D. A. Karmanov

摘要

Abstract

For a singularly perturbed reaction–diffusion equation with periodic coefficients, the structure of the inner transition layer in the case of a balanced reaction with a weak discontinuity is investigated. The existence of periodic solutions with an inner transition layers is proven, their stability is analyzed, and asymptotic approximations of solutions of this type are obtained. It is demonstrated that in the case of reaction balance, the presence of even a weak (asymptotically small) reaction discontinuity can lead to the formation of several periodic contrast structures of finite size, both stable and unstable.