{"title":"Perturbation at Blow-Up Time of Self-Similar Solutions for the Modified Korteweg–de Vries Equation","authors":"Simão Correia, Raphaël Côte","doi":"10.1007/s00205-024-01969-x","DOIUrl":null,"url":null,"abstract":"<div><p>We prove a first stability result of self-similar blow-up for the modified Korteweg–de Vries equation on the line. More precisely, given a self-similar solution and a sufficiently small regular profile, there is a unique global solution which behaves at <span>\\(t=0\\)</span> as the sum of the self-similar solution and the smooth perturbation.</p></div>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00205-024-01969-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 0
Abstract
We prove a first stability result of self-similar blow-up for the modified Korteweg–de Vries equation on the line. More precisely, given a self-similar solution and a sufficiently small regular profile, there is a unique global solution which behaves at \(t=0\) as the sum of the self-similar solution and the smooth perturbation.
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