Stationary isothermic surfaces for unbounded domains

• Autores: Rolando Magnanini , Shigeru Sakaguchi
• Localización: Indiana university mathematics journal, ISSN 0022-2518, Vol. 56, Nº 6, 2007, págs. 2723-2738
• Idioma: inglés
• DOI: 10.1512/iumj.2007.56.3150
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• Resumen

  • The initial temperature of a heat conductor is zero and its boundary temperature is kept equal to one at each time. The conductor contains a stationary isothermic surface, that is, an invariant spatial level surface of the temperature. In a previous paper, we proved that, if the conductor is bounded, then it must be a ball. Here, we prove that the boundary of the conductor is either a hyperplane or the union of two parallel hyperplanes when it is unbounded and satisfies certain global assumptions.