{"title":"Mathematical analysis of a fourth-order degenerate equation with a nonlinear second-order term","authors":"L. Kong, B. Liang, Y. Li, Y. Wang, Xiaoqin Wu","doi":"10.3233/jcm-226854","DOIUrl":null,"url":null,"abstract":"A fourth-order partial differential model in this paper is called the thin-film equation in the field of fluid theory. The existence of the weak solution is obtained by solving two approximation problems. In order to perform the limit for small parameters in the approximation problems, the Galerkin method and the entropy functional method are both used. By means of some classical compactness results we can give the existence of nonnegative weak solutions. Finally, by redefining the entropy functional, the long-time exponential decay is given in the sense of L1-norm.","PeriodicalId":45004,"journal":{"name":"Journal of Computational Methods in Sciences and Engineering","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2023-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Methods in Sciences and Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3233/jcm-226854","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
A fourth-order partial differential model in this paper is called the thin-film equation in the field of fluid theory. The existence of the weak solution is obtained by solving two approximation problems. In order to perform the limit for small parameters in the approximation problems, the Galerkin method and the entropy functional method are both used. By means of some classical compactness results we can give the existence of nonnegative weak solutions. Finally, by redefining the entropy functional, the long-time exponential decay is given in the sense of L1-norm.
期刊介绍：
The major goal of the Journal of Computational Methods in Sciences and Engineering (JCMSE) is the publication of new research results on computational methods in sciences and engineering. Common experience had taught us that computational methods originally developed in a given basic science, e.g. physics, can be of paramount importance to other neighboring sciences, e.g. chemistry, as well as to engineering or technology and, in turn, to society as a whole. This undoubtedly beneficial practice of interdisciplinary interactions will be continuously and systematically encouraged by the JCMSE.
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