Riassunto
Si studia un problema di Stefan a due fasi in uno strato piano indefinito, quando sia assegnata la temperatura sui piani che delimitano lo strato stesso.
Viene dimostrata l’esistenza (in grande) e l’unicità della soluzione sotto ipotesi assai generali sui dati iniziali ed al contorno. Sî prova la dipendenza continua e monotona della soluzione dai dati iniziali ed al contorno.
Abstract
We studied a two phase Stefan problem in a infinite plane slab, when the temperatures are prescribed on the two limiting planes.
We proved global existence and uniqueness of the solution under minimal smoothness assumptions upon the initial and boundary data. Furthermore, we demonstrated the continuous and monotone dependence of the solution on the initial and boundary data.
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Bibliografia
B. Budak andM. Z. Moskal,Classical solution of the multidimensional multifront Stefan problem, Soviet Math. Dokl., Vol. 10 (1969), #5, pp. 1043–1046.
J. R. Cannon,A priori estimate for continuation of the solution of the heat equation in the space variable, Ann. Mat. Pura Appl. 66 (1964), pp. 377–388.
J. R. Cannon, andJim Douglas, Jr.,The stability of the boundary in a Stefan problem, Ann. della Scuola normale Superiore di Pisa, Vol. XXI, Fasc I (1967), pp. 83–91.
J. R. Cannon andC. D. Hill,Existence, uniqueness, stability, and monotone dependence in a Stefan problem for the heat equation, J. of Math. and Mech. Vol. 17 (1967), pp. 1–20.
J. R. Cannon, Jim Douglas, Jr, andC. D. Hill,A multi-boundary Stefan problem and the disappearance of phases, J. of Math. and Mech., Vol. 17, (1967), pp. 21–34.
J. R. Cannon andC. D. Hill,Remarks on a Stefan problem, J. of Math. and Mech., Vol. 17, (1967), pp. 433–442.
—— ——,On the infinite differentiability of the free boundary in a Stefan problem, J. of Math. Anal and Appl., Vol. 22, (1968), pp. 385–397.
Avner Friedman,The Stefan problem in several space variables, Transaction of the A.M.S., Vol. 133, (1968), pp. 51–87.
—— ——,One dimensional Stefan problems with nonmonotone free boundary, Transactions of the A.M.S., Vol. 133, (1968), pp. 89–114.
—— ——,Correction to « the Stefan problem in several space variables », Transaction of A.M.S., Vol. 142, (1969), p. 557.
M. Gevrey,Sur les équations aux dérivées partielles du type parabolique, J. Math. (ser. 6), 9 (1913), pp. 305–471.
S. L. Kamenomostskaja,On Stefan’s problem, Mat. Sb. 53 (95) (1965), pp. 485–513.
Jiang Li-shang,Existence and differentiability of the solution of a two-phase Stefan problem for quasi-linear parabolic equations, Chinese Math. 7 (1965), pp, 481–496.
D. Quilghini,Una analisi fisico-matematica del processo del cambiamento di fase, Ann. di Mat. pura ed applicata, (IV), Vol. LXVII (1965), pp. 33–74.
L. I. Rubinstein,Two-phase Stefan problem on a segment with one-phase initial state of thermoconductive medium, Ucen, Zap. Lat. Gos. Univ. Stucki 58 (1964), pp. 111–148.
G. Sestini,Esistenza ed unicità nel problema di Stefan relativo a campi dotati di simmetria, Rivista Mat. Univ. Parma 3 (1952), pp. 103–113.
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Entrata in Redazione il 14 settembre 1970.
The research was supported in part by the National Science Foundation contract GP 15724 and the NATO Senior Fellowship program.
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Cannon, J.R., Primicerio, M. A two phase Stefan problem with temperature boundary conditions. Annali di Matematica 88, 177–191 (1971). https://doi.org/10.1007/BF02415066
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DOI: https://doi.org/10.1007/BF02415066