{"title":"特里贝尔-利佐金空间上的线性阻尼波方程求解","authors":"Meizhong Wang, Jiecheng Chen, Dashan Fan, Junyan Zhao","doi":"10.1007/s40840-024-01751-y","DOIUrl":null,"url":null,"abstract":"<p>In this article we study the solution <i>u</i>(<i>t</i>, <i>x</i>) of the Cauchy problem of linear damped wave equation. We obtain the sufficient and necessary condition of the boundedness of the solution <i>u</i>(<i>t</i>, <i>x</i>) on the Triebel–Lizorkin space at a fixed time <i>t</i>.</p>","PeriodicalId":50718,"journal":{"name":"Bulletin of the Malaysian Mathematical Sciences Society","volume":"15 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Solution of Linear Damped Wave Equation on Triebel–Lizorkin Spaces\",\"authors\":\"Meizhong Wang, Jiecheng Chen, Dashan Fan, Junyan Zhao\",\"doi\":\"10.1007/s40840-024-01751-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this article we study the solution <i>u</i>(<i>t</i>, <i>x</i>) of the Cauchy problem of linear damped wave equation. We obtain the sufficient and necessary condition of the boundedness of the solution <i>u</i>(<i>t</i>, <i>x</i>) on the Triebel–Lizorkin space at a fixed time <i>t</i>.</p>\",\"PeriodicalId\":50718,\"journal\":{\"name\":\"Bulletin of the Malaysian Mathematical Sciences Society\",\"volume\":\"15 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-08-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the Malaysian Mathematical Sciences Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s40840-024-01751-y\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Malaysian Mathematical Sciences Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s40840-024-01751-y","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Solution of Linear Damped Wave Equation on Triebel–Lizorkin Spaces
In this article we study the solution u(t, x) of the Cauchy problem of linear damped wave equation. We obtain the sufficient and necessary condition of the boundedness of the solution u(t, x) on the Triebel–Lizorkin space at a fixed time t.
期刊介绍：
This journal publishes original research articles and expository survey articles in all branches of mathematics. Recent issues have included articles on such topics as Spectral synthesis for the operator space projective tensor product of C*-algebras; Topological structures on LA-semigroups; Implicit iteration methods for variational inequalities in Banach spaces; and The Quarter-Sweep Geometric Mean method for solving second kind linear fredholm integral equations.
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