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タイトル: | Two-phase heat conductors with a stationary isothermic surface and their related elliptic overdetermined problems (Regularity, singularity and long time behavior for partial differential equations with conservation law) |
著者: | Sakaguchi, Shigeru |
キーワード: | 35K05 35K10 35B06 35B40 35K15 35K20 35J05 35J25 heat equation diffusion equation two-phase heat conductor transmission condition Cauchy problem two dimensions stationary isothermic surface symmetry elliptic overdetermined problem |
発行日: | Apr-2020 |
出版者: | Research Institute for Mathematical Sciences, Kyoto University |
誌名: | 数理解析研究所講究録別冊 |
巻: | B80 |
開始ページ: | 113 |
終了ページ: | 132 |
抄録: | We consider a two-phase heat conductor in two dimensions consisting of a core and a shell with different constant conductivities. When the medium outside the two-phase conductor has a possibly different conductivity, we consider the Cauchy problem in two dimensions where initially the conductor has temperature 0 and the outside medium has temperature 1. It is shown that, if there is a stationary isothermic surface in the shell near the boundary, then the structure of the conductor must be circular. Moreover, as by-products of the method of the proof, we mention other proofs of all the previous results of [S] in N(≥ 2) dimensions and two theorems on their related two-phase elliptic overdetermined problems. |
記述: | "Regularity, singularity and long time behavior for partial differential equations with conservation law". June 6-8, 2016. edited by Keiichi Kato, Mishio Kawashita, Masashi Misawa and Takayoshi Ogawa. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed. |
著作権等: | © 2020 by the Research Institute for Mathematical Sciences, Kyoto University. All rights reserved. |
URI: | http://hdl.handle.net/2433/260662 |
出現コレクション: | B80 Regularity, singularity and long time behavior for partial differential equations with conservation law |
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