Nonlinear stability of a quasi-static Stefan problem with surface tension : a continuation approach
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 30 (2001) no. 2, pp. 341-403. 
@article{ASNSP_2001_4_30_2_341_0,
     author = {Friedman, Avner and Reitich, Fernando},
     title = {Nonlinear stability of a quasi-static {Stefan} problem with surface tension : a continuation approach},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {341--403},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 30},
     number = {2},
     year = {2001},
     mrnumber = {1895715},
     zbl = {1072.35208},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2001_4_30_2_341_0/}
}
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Friedman, Avner; Reitich, Fernando. Nonlinear stability of a quasi-static Stefan problem with surface tension : a continuation approach. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 30 (2001) no. 2, pp. 341-403. http://www.numdam.org/item/ASNSP_2001_4_30_2_341_0/

[1] R.A. Adams, "Sobolev Spaces", Academic Press, New York, 1975. | MR | Zbl

[2] B.V. Bazalii, Stefan problem for the Laplace equation with regard for the curvature of the free boundary, Ukrainian Math. J. 49 (1997), 1465-1484. | MR | Zbl

[3] X. Chen, The Hele-Shaw problem and area-preserving curve-shortening motions, Arch. Rational Mech. Anal. 123 (1993), 117-151. | MR | Zbl

[4] X. Chen - J. Hong - F. Yi, Existence, uniqueness, and regularity of classical solutions of the Mullins-Sekerka problem, Comm. Partial Differential Equations 21 (1993), 1705-1727. | MR | Zbl

[5] X. Chen - F. Reitich, Local existence and uniqueness of solutions of Stefan problem with surface tension and kinetic undemooling, J. Math. Anal. Appl. 164 (1992), 350-362. | MR | Zbl

[6] P. Constantin - L. Kadanoff, Dynamics of a complex interface, Physica D 47 (1991), 450-460. | MR | Zbl

[7] P. Constantin - M. Pugh, Global solutions for small data to the Hele-Shaw problem, Nonlinearity 6 (1993), 393-415. | MR | Zbl

[8] J. Duchon - R. Robert, Evolution d'une interface par capillarité et diffusion de volume I. Existence locale en temps, Ann. Inst. H. Poincaré, Anal. non Linéaire 1 (1984) 361-378. | Numdam | MR | Zbl

[9] J. Escher - G. Simonett, Classical solutions of multidimensional Hele-Shaw models, SIAM J. Math. Anal. 28 (1997), 1028-1047. | MR | Zbl

[10] J. Esher - G. Simonett, A center manifold analysis for the Mullins-Sekerka model, J. Differential Equations 143 (1998), 267-292. | MR | Zbl

[11] A. Friedman - F. Reitich, Symmetry-breaking bifurcation of analytic solutions to free boundary problems: an application to a model of tumor growth, Trans. Amer. Math. Soc. 353 (2000), 1587-1634. | MR | Zbl

[12] D. Gilbarg - N.S. Trudinger, "Elliptic Partial Differential Equations of Second Order", Springer, Verlag, New York, 1983. | MR | Zbl

[ 13] S. Luckhaus, Solutions for the two-phase Stefan problem with Gibbs-Thomson law for the melting temperature, European J. Appl. Math. 1 (1990), 101-111. | MR | Zbl

[14] C. Müller, "Spherical Harmonics", Springer-Verlag, Berlin, 1966. | MR | Zbl

[15] E. Radkevitch, The Gibbs-Thomson correction and conditions for the classical solution of the modified Stefan problem, Soviet Math. Doklaly 43 (1991), 274-278. | MR | Zbl