Birth of a cusp in the two-dimensional, undercooled stefan problem

Quarterly of Applied Mathematics

Volumn 58, Issue 3, 2000, Pages 473-494

  Herrero, M A ^a   Medina, E ^b   Velazquez J J L ^a  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^b UNIVERSITY OF CÁDIZ   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; COOLING; EIGENVALUES AND EIGENFUNCTIONS; FOURIER TRANSFORMS; FUNCTION EVALUATION; INTEGRAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; POLYNOMIALS; TWO DIMENSIONAL;

CUSP; MATCHED ASYMPTOTIC EXPANSION; STEFAN PROBLEM; UNDERCOOLING;

PERTURBATION TECHNIQUES;

EID: 0034273927     PISSN: 0033569X     EISSN: None     Source Type: Journal    
DOI: 10.1090/qam/1770650     Document Type: Article

References (11)

1. D. Andreucci, M. A. Herrero, and J. J. L. Velázquez, The classical one-phase Stefan problem: A catalogue of interface behaviours, to appear
2. L. A. Caffarelli, The regularity of free boundaries in higher dimensions, Acta Math. 139, 155-184 (1977)
3. B. Caroli, C. Caroli, and B. Roulet, Instabilities of planar solidification fronts, In Solids Far from Equilibrium, C. Godrèche, editor, Cambridge University Press, 1992, pp. 155-296
4. A. Fasano, M. Primicerio, S. W. Howinson, and J. R. Ockendon, On the singularities of one-dimensional Stefan problems with undercooling, In Mathematical Models for Phase Change Problems (J. F. Rodrigues, ed.), International Series on Numerical Mathematics, vol. 88, Birkhäuser, 1989, pp. 215-226.
5. M. A. Herrero and J. J. L. Velázquez, Singularity formation in the one-dimensional supercooled Stefan problem, European Journal of Applied Math. 7, 119-150 (1996)
6. A. A. Lacey, Bounds on the solutions of one-phase Stefan problems, European Journal of Applied Math. 6, 509-516 (1995)
7. A. A. Lacey and J. R. Ockendon, Ill-posed free, boundary problems, Control and Cybernetics 14, 275-296 (1985)
8. W. W. Mullins and R. F. Sekerka, Stability of a planar interface during solidification of a dilute binary alloy, Journal of Applied Physics 35, 444-451 (1964)
9. P. Pelcé (editor), Dynamics of Curved Fronts, Academic Press, 1988
10. B. Sherman, A general one-phase Stefan problem, Quart. Appl. Math. 28, 377-383 (1970)
11. J. J. L. Velázquez, Cusp formation for the undercooled Stefan, problem in two and three dimensions, European Journal of Applied Math. 8, 1-21 (1997)