具有可变系数扩散的阻尼波方程的全局存在性和渐近曲线

Pub Date : 2024-01-08 DOI:10.58997/ejde.2024.04

Yuequn Li, Hui Liu, Fei Guo

{"title":"具有可变系数扩散的阻尼波方程的全局存在性和渐近曲线","authors":"Yuequn Li, Hui Liu, Fei Guo","doi":"10.58997/ejde.2024.04","DOIUrl":null,"url":null,"abstract":"We considered a Cauchy problem of a one-dimensional semilinear wave equation with variable-coefficient diffusion, time-dependent damping, and perturbations. The global well-posedness and the asymptotic profile are given by employing scaling variables and the energy method. The lower bound estimate of the lifespan to the solution is obtained as a byproduct. \nFor more information see https://ejde.math.txstate.edu/Volumes/2024/04/abstr.html","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Global existence and asymptotic profile for a damped wave equation with variable-coefficient diffusion\",\"authors\":\"Yuequn Li, Hui Liu, Fei Guo\",\"doi\":\"10.58997/ejde.2024.04\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We considered a Cauchy problem of a one-dimensional semilinear wave equation with variable-coefficient diffusion, time-dependent damping, and perturbations. The global well-posedness and the asymptotic profile are given by employing scaling variables and the energy method. The lower bound estimate of the lifespan to the solution is obtained as a byproduct. \\nFor more information see https://ejde.math.txstate.edu/Volumes/2024/04/abstr.html\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-01-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.58997/ejde.2024.04\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.58997/ejde.2024.04","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

我们考虑了一个一维半线性波方程的 Cauchy 问题，该方程具有可变系数扩散、随时间变化的阻尼和扰动。通过使用缩放变量和能量法，给出了全局好求和渐近曲线。作为副产品，还得到了求解寿命的下限估计值。更多信息，请参见 https://ejde.math.txstate.edu/Volumes/2024/04/abstr.html

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

Global existence and asymptotic profile for a damped wave equation with variable-coefficient diffusion

We considered a Cauchy problem of a one-dimensional semilinear wave equation with variable-coefficient diffusion, time-dependent damping, and perturbations. The global well-posedness and the asymptotic profile are given by employing scaling variables and the energy method. The lower bound estimate of the lifespan to the solution is obtained as a byproduct. For more information see https://ejde.math.txstate.edu/Volumes/2024/04/abstr.html

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助