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A two phase stefan problem: regularity of the free boundary

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Riassunto

Con riferimento ad un problema di Stefan a due fasi in uno strato piano indefinito, viene dimostrata la infinita differenziabilità della funzione x=s(t) che rappresenta ad ogni istante la ascissa del piano di separazione tra le due fasi.

La trattazione è valida sia per il caso in cui si assegni la temperatura sulle facce dello strato, sia per quello in cui venga assegnato il fiusso.

Abstract

We proved the infinite differentability of the function x=s(t) giving, for all t, the abscissa of the interface plane for a two phase Stefan problem in a plane infinite slab.

The proof applies in both cases of temperature or thermal fluxes prescribed on the two limiting planes.

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Additional information

The research was supported in part by the National Science Foundation contract GP 15724 and the NATO Senior Fellowship program.

Entrata in Redazione il 14 settembre 1970.

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Cannon, J.R., Primicerio, M. A two phase stefan problem: regularity of the free boundary. Annali di Matematica 88, 217–228 (1971) doi:10.1007/BF02415069

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Keywords

  • Free Boundary
  • Interface Plane
  • Thermal Flux
  • Stefan Problem
  • Infinite Slab