Abstract
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 the structure of the conductor must be spherical. Also, when the medium outside 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 temperature 1. Then we show that almost the same proposition holds true.
Original language | English |
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Pages (from-to) | 167-187 |
Number of pages | 21 |
Journal | Rendiconti dell'Istituto di Matematica dell'Universita di Trieste |
Volume | 48 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2016 |
Keywords
- Cauchy problem
- Diffusion equation
- Heat equation
- Initial-boundary value problem
- Stationary isothermic surface
- Symmetry
- Transmission condition
- Two-phase heat conductor
ASJC Scopus subject areas
- Mathematics(all)