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

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References | Similar Articles | Additional Information

**[1]**M. Bertsch, P. De. Mottoni, and L. A. Peletier,*Degenerate diffusion and the Stefan problem*, Nonlin. Anal.**8**, 1311-1336 (1984)**[2]**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)**[3]**B. D. Coleman and W. Noll,*The thermodynamics of elastic materials with heat conduction and viscosity*, Arch. Rational Mech. Anal.**13**, 245-261 (1963)**[4]**A. B. Crowley and J. R. Ockendon,*Modelling mushy regions*, Appl. Sci. Res.**44**, 1-7 (1987)**[5]**C. M. Dafermos,*Hyperbolic systems of balance laws*, Systems of Nonlinear Partial Differential Equations, J. M. Ball ed., Reidel, Dordrecht, 1983**[6]**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)**[7]**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)**[8]**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)**[9]**A. Fasano, M. Primicerio, and A. A. Lacey,*New results on some classical parabolic free boundary problems*, Quart. Appl. Math.**38**, 439-460 (1981)**[10]**A. Friedman,*Analyticity of the free boundary for the Stefan problem*, Arch. Rational Mech. Anal.**61**, 97-125 (1976)**[11]**M. E. Gurtin,*Multiphase thermomechanics with interfacial structure*. 1 .*Heat conduction and the capillarity balance law*, Arch. Rational. Mech. Anal.**104**, 195-221 (1988)**[12]**S. D. Howison, J. R. Ockendon, and A. A. Lacey,*Singularity development in moving boundary problems*, Quart. Appl. Math.**38**, 343-360 (1985)**[13]**A. A. Lacey and A. B. Taylor,*A mushy region in a Stefan problem*, IMA J. Appl. Math.**30**, 303-314 (1983)**[14]**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)**[15]**B. Sherman,*A general one-phase Stefan problem*, Quart. Appl. Math.**28**, 377-382 (1970)**[16]**M. Ughi,*A melting problem with a mushy region*, IMA J. Appl. Math.**33**, 135-152 (1984)**[17]**A. Visintin, A new model for supercooling and superheating effects, IMA J. Appl. Math.**36**, 141-157 (1984)**[18]**A. Visintin,*Stefan problem with surface tension*, Mathematical Models for Phase Change Problems, J. F. Rodrigues ed., Birkhäuser Verlag, New York, 1989**[19]**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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Additional Information

DOI:
https://doi.org/10.1090/qam/1262324

Article copyright:
© Copyright 1994
American Mathematical Society