{"title":"Interface disappearance in fast reaction limit","authors":"Yuki Tsukamoto","doi":"10.1016/j.nonrwa.2025.104333","DOIUrl":null,"url":null,"abstract":"<div><div>We study the singular limit problem referred to as the fast reaction limit. This problem has been extensively studied when the same reaction term is used in a two-component system. However, the behavior of the solution under different reaction terms remains not yet well understood. In this paper, we will consider the problem where the reaction term is represented by a power term. When the reaction term is appropriate, we prove that the initial interface disappears immediately, and the function converges to a solution that satisfies the heat equation.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104333"},"PeriodicalIF":1.8000,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Real World Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1468121825000197","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We study the singular limit problem referred to as the fast reaction limit. This problem has been extensively studied when the same reaction term is used in a two-component system. However, the behavior of the solution under different reaction terms remains not yet well understood. In this paper, we will consider the problem where the reaction term is represented by a power term. When the reaction term is appropriate, we prove that the initial interface disappears immediately, and the function converges to a solution that satisfies the heat equation.
期刊介绍：
Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems.
The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.
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