{"title":"Anisotropic parabolic-elliptic systems with degenerate thermal conductivity","authors":"H. Khelifi","doi":"10.1080/00036811.2023.2282140","DOIUrl":null,"url":null,"abstract":"AbstractIn this paper, we investigate the existence and regularity of a capacity solution for a coupled nonlinear anisotropic parabolic-elliptic system, where the elliptic component of the parabolic equation involves thermal conductivities ai(u) that satisfy lims→+∞ai(s)=0 for all i=1,…,N. We work with anisotropic Sobolev spaces and use Schauder's fixed-point theorem to find weak solutions to approximate problems. In addition, we validate the convergence of a subsequence of approximate solutions to a capacity solution.Keywords: Capacity solutionsanisotropic parabolic-elliptic equationsweak solutionsthermistor problemfixed-point theoremregularityMATHEMATICS SUBJECT CLASSIFICATIONs: 35K6535M1035K6035J60 AcknowledgmentsThe author is grateful to the referees for their constructive comments and suggestions.Disclosure statementNo potential conflict of interest was reported by the author(s).","PeriodicalId":55507,"journal":{"name":"Applicable Analysis","volume":"9 24","pages":"0"},"PeriodicalIF":1.1000,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applicable Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/00036811.2023.2282140","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
AbstractIn this paper, we investigate the existence and regularity of a capacity solution for a coupled nonlinear anisotropic parabolic-elliptic system, where the elliptic component of the parabolic equation involves thermal conductivities ai(u) that satisfy lims→+∞ai(s)=0 for all i=1,…,N. We work with anisotropic Sobolev spaces and use Schauder's fixed-point theorem to find weak solutions to approximate problems. In addition, we validate the convergence of a subsequence of approximate solutions to a capacity solution.Keywords: Capacity solutionsanisotropic parabolic-elliptic equationsweak solutionsthermistor problemfixed-point theoremregularityMATHEMATICS SUBJECT CLASSIFICATIONs: 35K6535M1035K6035J60 AcknowledgmentsThe author is grateful to the referees for their constructive comments and suggestions.Disclosure statementNo potential conflict of interest was reported by the author(s).
期刊介绍：
Applicable Analysis is concerned primarily with analysis that has application to scientific and engineering problems. Papers should indicate clearly an application of the mathematics involved. On the other hand, papers that are primarily concerned with modeling rather than analysis are outside the scope of the journal
General areas of analysis that are welcomed contain the areas of differential equations, with emphasis on PDEs, and integral equations, nonlinear analysis, applied functional analysis, theoretical numerical analysis and approximation theory. Areas of application, for instance, include the use of homogenization theory for electromagnetic phenomena, acoustic vibrations and other problems with multiple space and time scales, inverse problems for medical imaging and geophysics, variational methods for moving boundary problems, convex analysis for theoretical mechanics and analytical methods for spatial bio-mathematical models.
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