On the melting of ice balls

SIAM Journal on Mathematical Analysis

Volumn 28, Issue 1, 1997, Pages 1-32

  Herrero, Miguel A ^a   Velázquez, Juan J L ^a  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

A priori estimates; Asymptotic behavior; Matched asymptotic expansions; Stefan problem

Indexed keywords

EID: 0041158749     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141095282152     Document Type: Article

References (19)

1. D. G. ARONSON AND S. KAMIN, Disappearance of phase in the Stefan problem: One space dimension, preprint 614, Institute for Mathematics and Its Applications, University of Minnesota, Minneapolis, 1990.
2. S. B. ANGENENT AND J. J. L. VELÁZQUEZ, Degenerate neckpinches in mean curvature flow, J. Reine Angew. Math., to appear.
3. A. BRESSAN, On the asymptotic shape of blow up, Indiana University Math. J., 39 (1990), pp. 947-959.
4. A. BRESSAN, Stable blow up patterns, J. Differential Equations, 98 (1992), pp. 57-75.
5. G. B. DAVIES AND J. M. HILL, A moving boundary problem for the sphere, IMA J. Appl. Math., 29 (1982), pp. 99-111.
6. L. C. EVANS AND B. F. KNERR, Instantaneous shrinking of the support of nonnegative solutions to certain nonlinear parabolic equations and variational inequalities, Illinois J. Math., 23 (1979), pp. 153-166.
7. Y. GIGA AND R. V. KOHN, Asymptotically self-similar blow up of semilinear heat equations, Comm. Pure Appl. Math., 38 (1985), pp. 297-319.
8. J. M. HILL AND J. DEWYNNE, On an integral formulation for moving boundary problems, Quart. Appl. Math., XLI (1984), pp. 443-455.
9. J. M. HILL AND J. DEWYNNE, On the inward solidification of cylinders, Quart. Appl. Math., XLIV (1986), pp. 59-70.
10. M. A. HERRERO AND J. J. L. VELÁZQUEZ, Approaching an extinction point in one-dimensional semilinear heat equations with strong absorption, J. Math. Anal. Appl., 170 (1992), pp. 353-381.
11. M. A. HERRERO AND J. J. L. VELÁZQUEZ, Singularity formulation in the one-dimensional supercooled Stefan problem, European J. Appl. Math., 7 (1996), pp. 119-150.
12. M. A. HERRERO AND J. J. L. VELÁZQUEZ, Explosion de solutions d'equations paraboliques semilinéaires supercritiques, C. R. Acad. Sci. Paris Sér. I Math., 319 (1994), pp. 141-143.
13. N. N. LEBEDEV, Special Functions and Their Applications, Dover, New York, 1972.
14. A. M. MEIRMANOV, The Stefan Problem, Expositions in Mathematics Series, De Gruyter, Hawthorne, NY, 1992.
15. P. M. MORSE AND H. FESHBACH, Methods of Theoretical Physics, Vol. I, McGraw-Hill, New York, 1953.
16. L. I. RUBENSTEIN, The Stefan Problem, Transl. Math. Monographs 27, AMS, Providence, RI, 1971.
17. D. S. RYLEY, F. T. SMITH, AND G. POOTS, The inward solidification of spheres and circular cylinders, Internat. J. Heat Mass Transfer, 17 (1974), pp. 1507-1516.
18. A. M. SOWARD, A unified approach to Stefan's problem for spheres and cylinders, Proc. Royal Soc. London Ser. A, 373 (1980), pp. 131-147.
19. K. STEWARTSON AND R. T. WAECHTER, On Stefan's problem for spheres, Proc. Royal Soc. London Ser. A, 348 (1976), pp. 415-526.