@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://archive.numdam.org/item/ASNSP_2001_4_30_2_341_0/} }
TY - JOUR AU - Friedman, Avner AU - Reitich, Fernando TI - Nonlinear stability of a quasi-static Stefan problem with surface tension : a continuation approach JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2001 SP - 341 EP - 403 VL - 30 IS - 2 PB - Scuola normale superiore UR - http://archive.numdam.org/item/ASNSP_2001_4_30_2_341_0/ LA - en ID - ASNSP_2001_4_30_2_341_0 ER -
%0 Journal Article %A Friedman, Avner %A Reitich, Fernando %T Nonlinear stability of a quasi-static Stefan problem with surface tension : a continuation approach %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2001 %P 341-403 %V 30 %N 2 %I Scuola normale superiore %U http://archive.numdam.org/item/ASNSP_2001_4_30_2_341_0/ %G en %F ASNSP_2001_4_30_2_341_0
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://archive.numdam.org/item/ASNSP_2001_4_30_2_341_0/
[1] Sobolev Spaces", Academic Press, New York, 1975. | MR | Zbl
, "[2] 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] The Hele-Shaw problem and area-preserving curve-shortening motions, Arch. Rational Mech. Anal. 123 (1993), 117-151. | MR | Zbl
,[4] Existence, uniqueness, and regularity of classical solutions of the Mullins-Sekerka problem, Comm. Partial Differential Equations 21 (1993), 1705-1727. | MR | Zbl
- - ,[5] 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] Dynamics of a complex interface, Physica D 47 (1991), 450-460. | MR | Zbl
- ,[7] Global solutions for small data to the Hele-Shaw problem, Nonlinearity 6 (1993), 393-415. | MR | Zbl
- ,[8] 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] Classical solutions of multidimensional Hele-Shaw models, SIAM J. Math. Anal. 28 (1997), 1028-1047. | MR | Zbl
- ,[10] A center manifold analysis for the Mullins-Sekerka model, J. Differential Equations 143 (1998), 267-292. | MR | Zbl
- ,[11] 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] Elliptic Partial Differential Equations of Second Order", Springer, Verlag, New York, 1983. | MR | Zbl
- , "[ 13] 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] Spherical Harmonics", Springer-Verlag, Berlin, 1966. | MR | Zbl
, "[15] The Gibbs-Thomson correction and conditions for the classical solution of the modified Stefan problem, Soviet Math. Doklaly 43 (1991), 274-278. | MR | Zbl
,