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References
Alt A. W.,Stromunghen durch inhomogene poröse Medien mit Rand, J. Reine Ang. Math.,305 (1979), pp. 89–115.
Athanasopoulos I. -Caffarelli L. -Salsa S.,Caloric functions in Lipschitz domains and regularity of solutions of phase transition problems, Ann. Math.,143 (1996), pp. 413–434.
Athanasopoulos I. -Caffarelli L. -Salsa S.,Regularity of the free boundary in parabolic phase transition problems, Acta Math.,176 (1996), 245–282.
Cannon J. R. -DiBenedetto E.,On the existence of weak solutions to an n-dimensional Sefan problem with non-linear boundary conditions, SIAM J. Math. Anal.,11 (1980), pp. 632–645.
Damlamian A.,Some results on multi-phase Stefan problem, Comm. P.D.E.,2 (1977), pp. 1017–1044.
Danilyuk I. I.,On the Stefan problem, Russian Math. Surverys,40 (5) (1985), pp. 157–223.
DiBenedetto E.,Continuity of weak solutions to certain singular parabolic equations, Ann. Mat. Pura Appl., (IV),130 (1982), pp. 131–176.
DiBenedetto E. -Friedman A.,Periodic behaviour for the evolutionary dam problem and related free boundary problems, Comm. P.D.E.,11 (1986), pp. 1297–1377.
Friedman A.,Variational Principles and Free Boundary Problems, Wiley, New York (1982).
Götz I. G. -Zaltzman B. B.,Nonincrease of mushy region in a nonhomogeneous Stefan problem, Quart. Appl. Math.,49 (1991), pp. 741–746.
Lions J. L.,Contrôle des systèmes distribués singuliers, Gauthier-Villars, Paris (1983).
Ladyzenskaya O. A. -Solonnikov V. A. -Ural'seva N. N.,Linear and Quasilinear quations of Parabolic Type, A.M.S. Transl. Monog.,23 (1968), Providence.
Magenes E.,Problema di Stefan Bifase in più Variabili Spaziali, Le Matematiche (Catania),36 (1983), pp. 65–108.
Meirmanov A. M.,The Stefan Problem, Nauka, Novosibirk (1986) (English transi, W. de Gruyter, Berlin (1992)).
Nochetto R. H.,A class of non-degenerate two-phase Stefan problems in several space variables, Comm. P.D.E.,12 (1987), pp. 21–45.
Rodrigues J. F.,The Stefan problem revisited, Int. Ser. Numer. Math.,88 (1989), pp. 129–190, Birkhäuser, Basel.
Rodrigues J. F.,On a steady-state two-phase Stefan problem with extraction, Int. Ser. Numer. Math.,95 (1990), pp. 229–240, Birkhäuser, Basel.
Rodrigues J. F.,Stability of the free boundary in a two-phase continuous casting Stefan problem, Pitman Res. Notes, Math. Ser.,28 (1993), pp. 143–148 (see also Preprint #13, CMAF/Univ. Lisbon (1990)).
Rulla J.,Weak solutions to Stefan problems with prescribed convection, SIAM J. Math. Anal.,18 (1987), pp. 1784–1800.
Rodrigues J. F. -Yi F.,On a two-phase continuous casting Stefan problem with nonlinear flux, European J. Appl. Math.,1 (1990), pp. 259–279.
Rodrigues J. F. -Zaltzman B.,On classical solutions of the two-phase steady-state Stefan problem in strips, Non-linear Anal. Th. Meth. Appl.,19 (1992), pp. 207–218.
Rodrigues J. F. -Zaltzman B.,Free boundary optimal control in the multidimensional Stefan problem, Pitman Lect. Notes Math. Series,323 (1995), pp. 186–194.
Visintin A.,Sur le problème de Stefan avec flux non linéaire, Boll. Un. Mat. Ital.,18-C (1981), pp. 63–86.
Zaltzman B.,Multidimensional two-phase quasistationary Stefan problem, Manuscripta Math.,78 (1993), pp. 287–381 (see also Ph.D. Thesis, Novosibirsk Univ. (1989)).
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Rodrigues, J.F., Zaltzman, B. Regular solutions of a Stefan problem in strips. Annali di Matematica pura ed applicata 172, 165–189 (1997). https://doi.org/10.1007/BF01782611
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DOI: https://doi.org/10.1007/BF01782611