Some remarks on the regularization of supercooled one-phase Stefan problems in one dimension
Authors:
A. Fasano, M. Primicerio, S. D. Howison and J. R. Ockendon
Journal:
Quart. Appl. Math. 48 (1990), 153-168
MSC:
Primary 35R35; Secondary 35K05, 80A20
DOI:
https://doi.org/10.1090/qam/1040239
MathSciNet review:
MR1040239
Full-text PDF Free Access
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Additional Information
D. A. Tarzia, A Bibliography on Moving-free Boundary Problems for the Heat Diffusion Equation, Istituto Matematico “U. Dini", Firenze, 1988
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A. B. Crowley and J. R. Ockendon, Modelling mushy regions, Appl. Sci. Res. 44, 1–7 (1987)
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A. B. Crowley, Numerical solution of alloy solidification problems revisited, Free Boundary Problems: Applications and Theory (A. Bossavit et al. eds.), Res. Notes Math. 120, Pitman, 1985, pp. 122-131
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D. A. Tarzia, A Bibliography on Moving-free Boundary Problems for the Heat Diffusion Equation, Istituto Matematico “U. Dini", Firenze, 1988
C. M. Elliott and J. R. Ockendon, Weak and Variational Methods for Moving Boundary Problems, Res. Notes Math. 59, Pitman, Boston-London, 1982
A. Fasano and M. Primicerio, General free boundary problems for the heat equation, J. Math. Anal. Appl., Part I 57, 694–723; (1977) Part II 58, 202–231; (1977). Part III 59, 1–14 (1977)
A. Fasano, S. Kamin, and M. Primicerio, Regularity of weak solutions of one dimensional two-phase Stefan problems, Ann. Mat. Pura Appl. 115, 341–348 (1977)
A. Fasano, M. Primicerio, and A. A. Lacey, New results on some classical parabolic free-boundary problems, Quart. Appl. Math. 38, 439–460 (1981)
B. Sherman, A general one-phase Stefan problem, Quart. Appl. Math. 28, 377–382 (1970)
C. Baiocchi and G. A. Pozzi, An evolution variational inequality related to a diffusion-absorption problem, Appl. Math Optim. 2, 304–314 (1975)
P. Van Moerbeke, Optimal stopping and free boundary problems, Rocky Mountain J. Math. 4, 539–578 (1974)
A. Friedman, Parabolic variational inequalities in one space dimension and smoothness of the free boundary, J. Funct. Anal. 18, 151–176 (1975)
E. Di Benedetto and A. Friedman, The ill-posed Hele-shaw model and the Stefan problem for supercooled water, Trans. Amer. Math. Soc. 282, 183–204 (1984)
R. Jensen, Smoothness of the free boundary in the Stefan problem with supercooled water, Illinois J. Math. 22, 623–629 (1978)
J. S. Langer, Instabilities and pattern formation in crystal growth, Rev. Modern Phys. 52, 1–28 (1980)
A. Visintin, supercooling and superheating effects in phase transition, IMA J. Appl. Math. 35, 233–256 (1985)
A. Visintin, A new model for supercooling and superheating effects, IMA J. Appl. Math. 36, 141–157 (1986)
A. B. Crowley and J. R. Ockendon, Modelling mushy regions, Appl. Sci. Res. 44, 1–7 (1987)
A. Schatz, Free boundary problems of Stefan type with prescribed flux, J. Math. Anal. Appl. 28, 569–580 (1969)
A. Fasano, Alcune osservazioni su una classe di problemi a contorno libero per l’equazione del calore, Le Matematiche 29, 397–411 (1974)
J. Crank and R. S. Gupta, A moving boundary problem arising from the diffusion of oxygen in absorbing tissue, J. Inst. Math. Appl. 10, 19–33 (1972)
D. R. Atthey, A finite difference scheme for melting problems, J. Inst. Math. Appl. 13, 353–356 (1974)
M. Primicerio, Mushy region in phase change problems, Applied Nonlinear Functional Analysis: Variational Methods and Ill-Posed Problems, K. H. Hoffmann and R. Gorenflo (Eds.), Verlag Peter Lang, Frankfurt, 1983, pp. 251–269
A. M. Meirmanov, An example of nonexistence of a classical solution of the Stefan problem, Soviet Math. Dokl. 23, 564–566 (1981)
S. D. Howison, A. A. Lacey, and J. R. Ockendon, Singularity development in moving-boundary problems, Quart. J. Mech. Appl. Math. 38, 343–360 (1985)
S. D. Howison, Cusp development in Hele-Shaw flow with a free surface, SIAM J. Appl. Math. 46, 20–26 (1986)
A. Fasano and M. Primicerio, A critical case for the solvability of Stefan-like problems, Math. Methods Appl. Sci. 5, 84–96 (1983)
A. B. Crowley, Numerical solution of alloy solidification problems revisited, Free Boundary Problems: Applications and Theory (A. Bossavit et al. eds.), Res. Notes Math. 120, Pitman, 1985, pp. 122-131
W. Xie, The Stefan problem with a kinetic condition at the free boundary, to appear
D. G. Schaeffer, Some examples of singularities in a free boundary, Ann. Sc. Norm. Sup. Pisa (IV) 4, 133–144 (1977)
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© Copyright 1990
American Mathematical Society
