Anisotropic parabolic-elliptic systems with degenerate thermal conductivity

IF 1.1 4区数学 Q2 MATHEMATICS, APPLIED

Applicable Analysis Pub Date : 2023-11-11 DOI:10.1080/00036811.2023.2282140

H. Khelifi

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).

查看原文本刊更多论文

具有退化导热系数的各向异性抛物-椭圆体系

摘要本文研究了一类非线性各向异性抛物-椭圆耦合系统容量解的存在性和正则性，该系统的抛物方程的椭圆分量包含热导率ai(u)满足lims→+∞ai(s)=0，且对于所有i=1，…，N。我们研究各向异性Sobolev空间，并利用Schauder不动点定理寻找近似问题的弱解。此外，我们验证了一个容量解的近似解的子序列的收敛性。关键词:容量解、各向同性抛物-椭圆方程、解、热敏电阻问题、不动点定理、正则性数学学科分类:35K6535M1035K6035J60致谢感谢审稿人提出的建设性意见和建议。披露声明作者未报告潜在的利益冲突。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Applicable Analysis 数学-应用数学

CiteScore

2.60

自引率

9.10%

发文量

175

审稿时长

2 months

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.