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Title: Two-phase heat conductors with a stationary isothermic surface
Authors: Sakaguchi, Shigeru
Keywords: heat equationdiffusion equationtwo-phase heat conductortransmission conditioninitial-boundary value problemCauchy problemstationary isothermic surfacesymmetry
Issue Date: 2016
Publisher: EUT Edizioni Università di Trieste
Series/Report no.: Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics
48 (2016)
We consider a two-phase heat conductor in RN with N ≥ 2 consisting of a core and a shell with different constant conductivities. Suppose that, initially, the conductor has temperature 0 and, at all times, its boundary is kept at temperature 1. It is shown that, if there is a stationary isothermic surface in the shell near the boundary, then he structure of the conductor must be spherical. Also, when the medium utside the two-phase conductor has a possibly different conductivity, we consider the Cauchy problem with N ≥ 3 and the initial condition where the conductor has temperature 0 and the outside medium has emperature 1. Then we show that almost the same proposition holds true.
ISSN: 0049-4704
eISSN: 2464-8728
DOI: 10.13137/2464-8728/13155
Appears in Collections:Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics vol.48 (2016)

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