Morphological instability of similarity solution to the Stefan problem with undercooling and surface tension
Authors:
I. Rubinstein and B. Zaltzman
Journal:
Quart. Appl. Math. 56 (1998), 341-354
MSC:
Primary 35B35; Secondary 35K05, 35R35, 80A22
DOI:
https://doi.org/10.1090/qam/1622507
MathSciNet review:
MR1622507
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Abstract: This paper concerns morphological stability of a similarity solution to the Stefan problem with surface tension and initial supercooling. The linear stability analysis shows that for a nonzero surface tension each perturbation mode with a nonzero wave number is stable. However, the solution is unstable with respect to perturbations with a zero wave number limit point in their Fourier spectrum.
J. S. Langer, Instabilities and pattern formation in crystal growth, Rev. of Modern Physics 52 (1), 1–28 (1980)
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)
- L. Rubinstein, Global stability of the Neumann solution of the two-phase Stefan problem, IMA J. Appl. Math. 28 (1982), no. 3, 287–299. MR 666157, DOI https://doi.org/10.1093/imamat/28.3.287
- J. Chadam and P. Ortoleva, The stabilizing effect of surface tension on the development of the free boundary in a planar, one-dimensional, Cauchy-Stefan problem, IMA J. Appl. Math. 30 (1983), no. 1, 57–66. MR 711102, DOI https://doi.org/10.1093/imamat/30.1.57
W. Gautschi, Error function and Fresnel Integrals, in Handbook of Mathematical Functions, ed. by M. Abramowitz and I. A. Segun, Dover Publ., New York, 1968
J. S. Langer, Instabilities and pattern formation in crystal growth, Rev. of Modern Physics 52 (1), 1–28 (1980)
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)
L. Rubinstein, Global stability of the Neumann solution of the two-phase Stefan problem, IMA J. Appl. Math. 28 (3), 287–300 (1982)
J. Chadam and P. Ortoleva, The stabilizing effect of surface tension on the development of the free boundary in a planar one-dimensional Cauchy-Stefan problem, IMA J. Appl. Math. 30 (1), 57–65 (1983)
W. Gautschi, Error function and Fresnel Integrals, in Handbook of Mathematical Functions, ed. by M. Abramowitz and I. A. Segun, Dover Publ., New York, 1968
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Article copyright:
© Copyright 1998
American Mathematical Society
