{"title":"Blow-up of classical solutions of quasilinear wave equations in one space dimension","authors":"Yuki Haruyama , Hiroyuki Takamura","doi":"10.1016/j.nonrwa.2024.104212","DOIUrl":null,"url":null,"abstract":"<div><p>This paper studies the upper bound of the lifespan of classical solutions of the initial value problems for one dimensional wave equations with quasilinear terms of space-, or time-derivatives of the unknown function. The result for the space-derivative case guarantees the optimality of the general theory for nonlinear wave equations, and its proof is carried out by combination of ordinary differential inequality and iteration method on the lower bound of the weighted functional of the solution.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"81 ","pages":"Article 104212"},"PeriodicalIF":1.8000,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1468121824001512/pdfft?md5=8d3c17560b8046622b27bc7b02e5e3fe&pid=1-s2.0-S1468121824001512-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Real World Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1468121824001512","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
This paper studies the upper bound of the lifespan of classical solutions of the initial value problems for one dimensional wave equations with quasilinear terms of space-, or time-derivatives of the unknown function. The result for the space-derivative case guarantees the optimality of the general theory for nonlinear wave equations, and its proof is carried out by combination of ordinary differential inequality and iteration method on the lower bound of the weighted functional of the solution.
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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