On the Mullins-Sekerka model for phase transitions in mixtures
Author:
Natasa Milic
Journal:
Quart. Appl. Math. 49 (1991), 437-445
MSC:
Primary 80A22; Secondary 80A15
DOI:
https://doi.org/10.1090/qam/1121676
MathSciNet review:
MR1121676
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Abstract: The Mullins-Sekerka model for dynamical phase transitions in two-component mixtures is considered. Global growth conditions for the phase regions and the interface are obtained from underlying conservation laws. A quasi-static model is formulated and the solutions are discussed for totally isolated mixtures.
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M. E. Gurtin, A. Struthers, and W. O. Williams, A transport theorem for moving interfaces (forthcoming)
J. W. Gibbs, On the equilibrium of heterogeneous substances, Trans. Connecticut Acad. 3, 108–248 (1876), 343–524 (1878). Reprinted in The Scientific Papers of J. Willard Gibbs, Vol. 1, Dover, New York, 1961
W. W. Mullins and R. F. Sekerka, Morphological stability of a particle growing by diffusion or heat flow, J. Appl. Phys. 34, 323–329 (1963)
R. F. Sekerka, Morphological stability, J. Crystal Growth (3) 4, 71–81 (1968)
R. F. Sekerka, Morphological stability, Crystal Growth: an Introduction, North-Holland, Amsterdam, 1973
N. Weck, Uber das Prinzip der eindeutigen Fortsetzbarkeit in der Kontrolltheorie, Optimization and Optimal Control, Lecture Notes in Math., vol. 477, Springer-Verlag, Berlin, 1975, pp. 276–284
E. J. P. Georg Schmidt and N. Weck, On the boundary behavior of solutions to elliptic and parabolic equations—with application to boundary control for parabolic equations, SIAM J. Control Optim. 16, 593–598 (1978)
R. F. Sekerka, Morphological instabilities during phase transformations, Phase Transformations and Material Instabilities in Solids (M. E. Gurtin, ed.), Academic Press, New York, 1984
M. E. Gurtin, On the theory of phase transitions with interfacial energy, Arch. Rational Mech. Anal. 87 187–212 (1985)
M. E. Gurtin, On the two-phase Stefan problem with interfacial energy and entropy, Arch. Rational Mech. Anal. 96, 199–241 (1986)
M. E. Gurtin, Multiphase thermomechanics with interfacial structure: Heat conduction and capillary balance law (forthcoming)
N. Milic, On the non-equilibrium phase-transitions in mixtures with interfacial structure, Ph.D. Thesis, Carnegie-Mellon University, Pittsburgh, PA, 1988
M. E. Gurtin, A. Struthers, and W. O. Williams, A transport theorem for moving interfaces (forthcoming)
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Article copyright:
© Copyright 1991
American Mathematical Society
