具有非局部弱阻尼的五元波方程动力学

arXiv - MATH - Dynamical Systems Pub Date : 2024-09-16 DOI:arxiv-2409.10035

Feng Zhou, Hongfang Li, Kaixuan Zhu, Xinyu Mei

{"title":"具有非局部弱阻尼的五元波方程动力学","authors":"Feng Zhou, Hongfang Li, Kaixuan Zhu, Xinyu Mei","doi":"arxiv-2409.10035","DOIUrl":null,"url":null,"abstract":"This article presents a new scheme for studying the dynamics of a quintic\nwave equation with nonlocal weak damping in a 3D smooth bounded domain. As an\napplication, the existence and structure of weak, strong, and exponential\nattractors for the solution semigroup of this equation are obtained. The\ninvestigation sheds light on the well-posedness and long-time behavior of\nnonlinear dissipative evolution equations with nonlinear damping and critical\nnonlinearity.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"143 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Dynamics of the quintic wave equation with nonlocal weak damping\",\"authors\":\"Feng Zhou, Hongfang Li, Kaixuan Zhu, Xinyu Mei\",\"doi\":\"arxiv-2409.10035\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This article presents a new scheme for studying the dynamics of a quintic\\nwave equation with nonlocal weak damping in a 3D smooth bounded domain. As an\\napplication, the existence and structure of weak, strong, and exponential\\nattractors for the solution semigroup of this equation are obtained. The\\ninvestigation sheds light on the well-posedness and long-time behavior of\\nnonlinear dissipative evolution equations with nonlinear damping and critical\\nnonlinearity.\",\"PeriodicalId\":501035,\"journal\":{\"name\":\"arXiv - MATH - Dynamical Systems\",\"volume\":\"143 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Dynamical Systems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.10035\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Dynamical Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10035","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

本文提出了一种研究三维光滑有界域中具有非局部弱阻尼的五次波方程动力学的新方案。作为应用，得到了该方程的解半群的弱矢量、强矢量和指数矢量的存在性和结构。该研究揭示了具有非线性阻尼和临界非线性的非线性耗散演化方程的良好求解性和长期行为。

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

本刊更多论文

Dynamics of the quintic wave equation with nonlocal weak damping

This article presents a new scheme for studying the dynamics of a quintic wave equation with nonlocal weak damping in a 3D smooth bounded domain. As an application, the existence and structure of weak, strong, and exponential attractors for the solution semigroup of this equation are obtained. The investigation sheds light on the well-posedness and long-time behavior of nonlinear dissipative evolution equations with nonlinear damping and critical nonlinearity.

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

来源期刊

arXiv - MATH - Dynamical Systems

自引率

0.00%

发文量