{"title":"A characterization of a hyperplane in two-phase heat conductorsu","authors":"Cavallina,Lorenzo, Sakaguchi,Shigeru, Udagawa,Seiichi","doi":"10.4310/cag.2023.v31.n7.a9","DOIUrl":null,"url":null,"abstract":"We consider the Cauchy problem for the heat diffusion equation in the whole Euclidean space consisting of two media with different constant conductivities, where initially one has temperature 0 and the other has temperature 1. Suppose that the interface is connected and uniformly of class $C^{6}$. We show that if the interface has a time-invariant constant temperature, then it must be a hyperplane.","PeriodicalId":50662,"journal":{"name":"Communications in Analysis and Geometry","volume":"10 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Analysis and Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/cag.2023.v31.n7.a9","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
We consider the Cauchy problem for the heat diffusion equation in the whole Euclidean space consisting of two media with different constant conductivities, where initially one has temperature 0 and the other has temperature 1. Suppose that the interface is connected and uniformly of class $C^{6}$. We show that if the interface has a time-invariant constant temperature, then it must be a hyperplane.
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