Nonlinear stability of a quasi-static Stefan problem with surface tension : a continuation approach

Avner Friedman; Fernando Reitich

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2001)

  • Volume: 30, Issue: 2, page 341-403
  • ISSN: 0391-173X

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Friedman, Avner, and 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 30.2 (2001): 341-403. <http://eudml.org/doc/84445>.

@article{Friedman2001,
author = {Friedman, Avner, Reitich, Fernando},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {2},
pages = {341-403},
publisher = {Scuola normale superiore},
title = {Nonlinear stability of a quasi-static Stefan problem with surface tension : a continuation approach},
url = {http://eudml.org/doc/84445},
volume = {30},
year = {2001},
}

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
PB - Scuola normale superiore
VL - 30
IS - 2
SP - 341
EP - 403
LA - eng
UR - http://eudml.org/doc/84445
ER -

References

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  8. [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 Linéaire1 (1984) 361-378. Zbl0572.35051MR779874
  9. [9] J. Escher - G. Simonett, Classical solutions of multidimensional Hele-Shaw models, SIAM J. Math. Anal.28 (1997), 1028-1047. Zbl0888.35142MR1466667
  10. [10] J. Esher - G. Simonett, A center manifold analysis for the Mullins-Sekerka model, J. Differential Equations143 (1998), 267-292. Zbl0896.35142MR1607952
  11. [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. Zbl0983.35019MR1806728
  12. [12] D. Gilbarg - N.S. Trudinger, "Elliptic Partial Differential Equations of Second Order", Springer, Verlag, New York, 1983. Zbl0562.35001MR737190
  13. [ 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. Zbl0734.35159MR1117346
  14. [14] C. Müller, "Spherical Harmonics", Springer-Verlag, Berlin, 1966. Zbl0138.05101MR199449
  15. [15] E. Radkevitch, The Gibbs-Thomson correction and conditions for the classical solution of the modified Stefan problem, Soviet Math. Doklaly43 (1991), 274-278. Zbl0782.35087MR1122261

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