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.
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.
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References
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The research was supported in part by the National Science Foundation contract G1 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 with flux boundary conditions. Annali di Matematica 88, 193–205 (1971). https://doi.org/10.1007/BF02415067
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DOI: https://doi.org/10.1007/BF02415067