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Annali di Matematica Pura ed Applicata

, Volume 88, Issue 1, pp 193–205 | Cite as

A two phase Stefan problem with flux boundary conditions

  • John R. Cannon
  • Mario Primicerio
Article

Abstract

We studied a two phase Stefan problem in a infinite plane slab, when the thermal fluxes are assigned on the two limiting planes.

We proved existence and uniqueness of the solution upon minimal smoothness assumptions upon the initial and boundary data, and we demonstrated the continuous and monotone dependence of the solution on the data.

In sec. 5 we studied in which cases one of the two phases disappears and the asymptotic behavior in the cases in which the two phases exist for all time.

Keywords

Boundary Condition Asymptotic Behavior Boundary Data Thermal Flux Stefan Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Riassunto

Si studia un problema di Stefan a due fasi in uno strato piano indefinito quando si suppongono assegnati i flussi termici sui piani che delimitano lo strato stesso.

Viene dimostrata l’esistenza e l’unicità della soluzione con ipotesi assai generali sui dati iniziali ed al contorno del problema, nonchè la dipendenza continua e monotona della soluzione da tali dati.

Si esaminano infine i casi in cui una delle due fasi può sparire ed il comportamento asintotico in caso di permanenza delle due fasi.

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Copyright information

© Nicola Zanichelli Editore 1971

Authors and Affiliations

  • John R. Cannon
    • 1
  • Mario Primicerio
    • 2
  1. 1.Mathematics DepartmentUniversity of Texas at AustinAustin
  2. 2.Istituto Matematico « Ulisse Dini »Università di FirenzeFirenzeItaly

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