{"title":"The Life Span of Classical Solutions to Nonlinear Wave Equations with Weighted Terms in Three Space Dimensions","authors":"Hu Sheng Wang, Fan Lü","doi":"10.1007/s10114-024-2600-9","DOIUrl":null,"url":null,"abstract":"<div><p>The paper considers the Cauchy problem with small initial values for semilinear wave equations with weighted nonlinear terms. Similar to Strauss exponent <i>p</i><sub>0</sub>(<i>n</i>) which is the positive root of the quadratic equation <span>\\(1+{1\\over 2}(n+1)p-{1\\over 2}(n-1)p^{2}=0\\)</span>, we get smaller critical exponents <i>p</i><sub><i>m</i></sub>(<i>n</i>),<i>p</i><span>\n <sup>*</sup><sub><i>m</i></sub>\n \n </span>(<i>n</i>) and have global existence in time when <i>p</i>><i>p</i><sub><i>m</i></sub>(<i>n</i>) or <i>p</i>><i>p</i><span>\n <sup>*</sup><sub><i>m</i></sub>\n \n </span>(<i>n</i>). In addition, for the blow-up case, the introduction of the spacial weight shows the optimality of new upper and lower bound.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 12","pages":"2984 - 3002"},"PeriodicalIF":0.8000,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Sinica-English Series","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10114-024-2600-9","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
The paper considers the Cauchy problem with small initial values for semilinear wave equations with weighted nonlinear terms. Similar to Strauss exponent p0(n) which is the positive root of the quadratic equation \(1+{1\over 2}(n+1)p-{1\over 2}(n-1)p^{2}=0\), we get smaller critical exponents pm(n),p*m(n) and have global existence in time when p>pm(n) or p>p*m(n). In addition, for the blow-up case, the introduction of the spacial weight shows the optimality of new upper and lower bound.
期刊介绍：
Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.
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