{"title":"Global Existence and Blow-up of Solutions for a Class of Singular Parabolic Equations with Viscoelastic Term","authors":"Yanchao Gao, Wenxu Jia, Zhixin Feng","doi":"10.1155/2024/5754129","DOIUrl":null,"url":null,"abstract":"In this paper, we consider the initial boundary value problem for a class of singular parabolic equations with viscoelastic term and logarithmic term. By using the technique of cut-off and the method of Faedo-Galerkin approximation, the local existence of the weak solution is established. Based on the potential well method, the global existence of the weak solution is derived. Furthermore, we prove that the weak solution blows up in finite time by taking the concavity analysis method.","PeriodicalId":15840,"journal":{"name":"Journal of Function Spaces","volume":"1 1","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Function Spaces","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1155/2024/5754129","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we consider the initial boundary value problem for a class of singular parabolic equations with viscoelastic term and logarithmic term. By using the technique of cut-off and the method of Faedo-Galerkin approximation, the local existence of the weak solution is established. Based on the potential well method, the global existence of the weak solution is derived. Furthermore, we prove that the weak solution blows up in finite time by taking the concavity analysis method.
期刊介绍：
Journal of Function Spaces (formerly titled Journal of Function Spaces and Applications) publishes papers on all aspects of function spaces, functional analysis, and their employment across other mathematical disciplines. As well as original research, Journal of Function Spaces also publishes focused review articles that assess the state of the art, and identify upcoming challenges and promising solutions for the community.
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