Two-phase heat conductors with a stationary isothermic surface

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3 Citations (Scopus)


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 languageEnglish
Pages (from-to)167-187
Number of pages21
JournalRendiconti dell'Istituto di Matematica dell'Universita di Trieste
Issue number1
Publication statusPublished - 2016


  • 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)


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