{"title":"Estimates of Lifespan and Blow-up Rates for the Wave Equation with a Time-dependent Damping and a Power-type Nonlinearity","authors":"K. Fujiwara, M. Ikeda, Yuta Wakasugi","doi":"10.1619/fesi.62.157","DOIUrl":null,"url":null,"abstract":"We study blow-up behavior of solutions for the Cauchy problem of the semilinear wave equation with time-dependent damping. When the damping is effective, and the nonlinearity is subcritical, we show the blow-up rates and the sharp lifespan estimates of solutions. Upper estimates are proved by an ODE argument, and lower estimates are given by a method of scaling variables.","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":"1 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2016-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1619/fesi.62.157","citationCount":"28","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Funkcialaj Ekvacioj-Serio Internacia","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1619/fesi.62.157","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 28
Abstract
We study blow-up behavior of solutions for the Cauchy problem of the semilinear wave equation with time-dependent damping. When the damping is effective, and the nonlinearity is subcritical, we show the blow-up rates and the sharp lifespan estimates of solutions. Upper estimates are proved by an ODE argument, and lower estimates are given by a method of scaling variables.
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