Thermodynamics and the supercritical Stefan equations with nucleations
Author:
Morton E. Gurtin
Journal:
Quart. Appl. Math. 52 (1994), 133-155
MSC:
Primary 80A22; Secondary 73B30
DOI:
https://doi.org/10.1090/qam/1262324
MathSciNet review:
MR1262324
Full-text PDF Free Access
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Additional Information
M. Bertsch, P. De. Mottoni, and L. A. Peletier, Degenerate diffusion and the Stefan problem, Nonlin. Anal. 8, 1311–1336 (1984)
M. Bertsch, P. De. Mottoni, and L. A. Peletier, The Stefan problem with heating: Appearance and disappearance of a mushy region, Trans. Amer. Math. Soc. 293, 677–691 (1986)
B. D. Coleman and W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal. 13, 245–261 (1963)
A. B. Crowley and J. R. Ockendon, Modelling mushy regions, Appl. Sci. Res. 44, 1–7 (1987)
C. M. Dafermos, Hyperbolic systems of balance laws, Systems of Nonlinear Partial Differential Equations, J. M. Ball ed., Reidel, Dordrecht, 1983
J. N. Dewynne, S. D. Howison, J. R. Ockendon, and W. Xie, Asymptotic behavior of solutions to the Stefan problem with a kinetic condition at the free boundary, J. Austral. Math. Soc. Ser. B 31, 81–96 (1989)
A. Fasano and M. Primicerio, General free boundary problems for the heat equation, Parts 1–3, J. Math. Anal. Appl. 57, 694–723; 58, 202–231; 59, 1–14 (1977)
A. Fasano, M. Primicerio, S. D. Howison, and J. R. Ockendon, Some remarks on the regularization of supercooled one-phase Stefan problems in one dimension, Quart. Appl. Math. 48, 153–168 (1990)
A. Fasano, M. Primicerio, and A. A. Lacey, New results on some classical parabolic free boundary problems, Quart. Appl. Math. 38, 439–460 (1981)
A. Friedman, Analyticity of the free boundary for the Stefan problem, Arch. Rational Mech. Anal. 61, 97–125 (1976)
M. E. Gurtin, Multiphase thermomechanics with interfacial structure. 1 . Heat conduction and the capillarity balance law, Arch. Rational. Mech. Anal. 104, 195–221 (1988)
S. D. Howison, J. R. Ockendon, and A. A. Lacey, Singularity development in moving boundary problems, Quart. Appl. Math. 38, 343–360 (1985)
A. A. Lacey and A. B. Taylor, A mushy region in a Stefan problem, IMA J. Appl. Math. 30, 303–314 (1983)
S. Luckhaus, Solutions for the two-phase Stefan problem with the Gibbs-Thomson law for the melting temperature, Euro. J. Appl. Math. 1, 101–111 (1990)
B. Sherman, A general one-phase Stefan problem, Quart. Appl. Math. 28, 377–382 (1970)
M. Ughi, A melting problem with a mushy region, IMA J. Appl. Math. 33, 135–152 (1984)
A. Visintin, A new model for supercooling and superheating effects, IMA J. Appl. Math. 36, 141-157 (1984)
A. Visintin, Stefan problem with surface tension, Mathematical Models for Phase Change Problems, J. F. Rodrigues ed., Birkhäuser Verlag, New York, 1989
A. Visintin, Surface tension effects in phase transition, Material Instabilities in Continuum Mechanics, J. M. Ball ed., Clarendon Press, New York, 1988
M. Bertsch, P. De. Mottoni, and L. A. Peletier, Degenerate diffusion and the Stefan problem, Nonlin. Anal. 8, 1311–1336 (1984)
M. Bertsch, P. De. Mottoni, and L. A. Peletier, The Stefan problem with heating: Appearance and disappearance of a mushy region, Trans. Amer. Math. Soc. 293, 677–691 (1986)
B. D. Coleman and W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal. 13, 245–261 (1963)
A. B. Crowley and J. R. Ockendon, Modelling mushy regions, Appl. Sci. Res. 44, 1–7 (1987)
C. M. Dafermos, Hyperbolic systems of balance laws, Systems of Nonlinear Partial Differential Equations, J. M. Ball ed., Reidel, Dordrecht, 1983
J. N. Dewynne, S. D. Howison, J. R. Ockendon, and W. Xie, Asymptotic behavior of solutions to the Stefan problem with a kinetic condition at the free boundary, J. Austral. Math. Soc. Ser. B 31, 81–96 (1989)
A. Fasano and M. Primicerio, General free boundary problems for the heat equation, Parts 1–3, J. Math. Anal. Appl. 57, 694–723; 58, 202–231; 59, 1–14 (1977)
A. Fasano, M. Primicerio, S. D. Howison, and J. R. Ockendon, Some remarks on the regularization of supercooled one-phase Stefan problems in one dimension, Quart. Appl. Math. 48, 153–168 (1990)
A. Fasano, M. Primicerio, and A. A. Lacey, New results on some classical parabolic free boundary problems, Quart. Appl. Math. 38, 439–460 (1981)
A. Friedman, Analyticity of the free boundary for the Stefan problem, Arch. Rational Mech. Anal. 61, 97–125 (1976)
M. E. Gurtin, Multiphase thermomechanics with interfacial structure. 1 . Heat conduction and the capillarity balance law, Arch. Rational. Mech. Anal. 104, 195–221 (1988)
S. D. Howison, J. R. Ockendon, and A. A. Lacey, Singularity development in moving boundary problems, Quart. Appl. Math. 38, 343–360 (1985)
A. A. Lacey and A. B. Taylor, A mushy region in a Stefan problem, IMA J. Appl. Math. 30, 303–314 (1983)
S. Luckhaus, Solutions for the two-phase Stefan problem with the Gibbs-Thomson law for the melting temperature, Euro. J. Appl. Math. 1, 101–111 (1990)
B. Sherman, A general one-phase Stefan problem, Quart. Appl. Math. 28, 377–382 (1970)
M. Ughi, A melting problem with a mushy region, IMA J. Appl. Math. 33, 135–152 (1984)
A. Visintin, A new model for supercooling and superheating effects, IMA J. Appl. Math. 36, 141-157 (1984)
A. Visintin, Stefan problem with surface tension, Mathematical Models for Phase Change Problems, J. F. Rodrigues ed., Birkhäuser Verlag, New York, 1989
A. Visintin, Surface tension effects in phase transition, Material Instabilities in Continuum Mechanics, J. M. Ball ed., Clarendon Press, New York, 1988
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© Copyright 1994
American Mathematical Society
