A symmetry theorem in two-phase heat conductors
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 medium has temperature 0 and the other has temperature 1. Under the assumptions that one medium is bounded and the interface...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-09-01
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| Series: | Mathematics in Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mine.2023061?viewType=HTML |
| _version_ | 1797659027464781824 |
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| author | Hyeonbae Kang Shigeru Sakaguchi |
| author_facet | Hyeonbae Kang Shigeru Sakaguchi |
| author_sort | Hyeonbae Kang |
| collection | DOAJ |
| description | 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 medium has temperature 0 and the other has temperature 1. Under the assumptions that one medium is bounded and the interface is of class $ C^{2, \alpha} $, we show that if the interface is stationary isothermic, then it must be a sphere. The method of moving planes due to Serrin is directly utilized to prove the result. |
| first_indexed | 2024-03-11T18:08:01Z |
| format | Article |
| id | doaj.art-2afff68b157e4c66b8ab1688927edb96 |
| institution | Directory Open Access Journal |
| issn | 2640-3501 |
| language | English |
| last_indexed | 2024-03-11T18:08:01Z |
| publishDate | 2023-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj.art-2afff68b157e4c66b8ab1688927edb962023-10-17T01:20:06ZengAIMS PressMathematics in Engineering2640-35012023-09-01531710.3934/mine.2023061A symmetry theorem in two-phase heat conductorsHyeonbae Kang0Shigeru Sakaguchi 11. Department of Mathematics and Institute of Applied Mathematics, Inha University, Incheon 22212, S. Korea2. Graduate School of Information Sciences, Tohoku University, Sendai, 980-8579, JapanWe 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 medium has temperature 0 and the other has temperature 1. Under the assumptions that one medium is bounded and the interface is of class $ C^{2, \alpha} $, we show that if the interface is stationary isothermic, then it must be a sphere. The method of moving planes due to Serrin is directly utilized to prove the result.https://www.aimspress.com/article/doi/10.3934/mine.2023061?viewType=HTMLheat diffusion equationtwo-phase heat conductorscauchy problemstationary isothermic surfacemethod of moving planestransmission conditions |
| spellingShingle | Hyeonbae Kang Shigeru Sakaguchi A symmetry theorem in two-phase heat conductors Mathematics in Engineering heat diffusion equation two-phase heat conductors cauchy problem stationary isothermic surface method of moving planes transmission conditions |
| title | A symmetry theorem in two-phase heat conductors |
| title_full | A symmetry theorem in two-phase heat conductors |
| title_fullStr | A symmetry theorem in two-phase heat conductors |
| title_full_unstemmed | A symmetry theorem in two-phase heat conductors |
| title_short | A symmetry theorem in two-phase heat conductors |
| title_sort | symmetry theorem in two phase heat conductors |
| topic | heat diffusion equation two-phase heat conductors cauchy problem stationary isothermic surface method of moving planes transmission conditions |
| url | https://www.aimspress.com/article/doi/10.3934/mine.2023061?viewType=HTML |
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