Phase transition with supercooling

 Access to full text

 Full (PDF)

 Full (DjVu)

1. ANDREUCCI, D., Continuation of the solution of a free boundary problem in cylindrical symmetry, Meccanica, 19 (1984), 91-97. Zbl0575.76130MR767042
2. ANDREUCCI, D.- FASANO, A.- PRIMICERIO, M.- RICCI, R., Mathematical problems in polymers crystallization, Survey Math. Ind., 6 (1996), 7-20. Zbl0846.35057MR1395851
3. ANDREUCCI, D.- HERRERO, M. A.- VELÁZQUEZ, J. J. L., Liouville theorems and blow up behaviour in semilinear reaction diffusion systems, Ann. Inst. Poincaré, 14 (1997), 1-53. Zbl0877.35019MR1437188
4. ANGENENT, S. B.- VELÁZQUEZ, J. J. L., Degerate neckpinches in mean curvature flow, to appear in J. Rheine Angew. Math. Zbl0866.58055MR1427656
5. ANGENENT, S. B.- VELÁZQUEZ, J. J. L., Asymptotic shape of cusp singularities in curve shortening, Duke Univ. Math. J., 77 (1), (1995), 71-110. Zbl0829.35058MR1317628
6. BAIOCCHI, C.- POZZI, G. A., An evolution variational inequality related to a diffusionabsorption problem, Appl. Math. Optim., 4 (1976), 304-314. Zbl0379.49014MR430538
7. CRANK, J.- GUPTA, R. S., A moving boundary problem arising from the diffusion of oxygen in absorbing tissues, J. Inst. Math. Appl., 10 (1972), 19-33. Zbl0247.65064MR347105
8. FASANO, A., Modelling the solidification of polymers: an example of an ECMI cooperation, ICIAM 91, R. E. O'MALLEY ed., SIAM, Philadelphia (1991), pp. 99-118. 
9. FASANO, A., Alcune osservazioni su una classe di problemi a contorno libero per l'equazione del calore, Le Matematiche, 29 (1974), 397-411. Zbl0313.35038MR410085
10. FASANO, A.- PRIMICERIO, M., Cauchy type free boundary problems for nonlinear parabolic equations, Riv. Mat. Univ. Parma, 5 (1979), 615-634. Zbl0699.35148MR584232
11. FASANO, A.- PRIMICERIO, M., An analysis of phase transition models, EJAM, 7 (1996), pp. 1-12. Zbl0858.34006MR1419642
12. FASANO, A.- PRIMICERIO, M., A critical case for the solvability of Stefan like problems, Math. Meth. Appl. Sci., 5 (1983), 84-96. Zbl0526.35078MR690897
13. FASANO, A.- PRIMICERIO, M., On a class of travelling wave solutions to phase change problems with an order parameter, Workshop on Nonlinear Analysis and Applications, N. KENMOCKI and M. NIETZGODKA eds., Warsaw (1995), pp. 113-123. Zbl0876.35051MR1422930
14. FASANO, A., PRIMICERIO, M., HOWISON, S. - OCKENDON, J., Some remarks on the regularization of supercooled one-phase Stefan problems in one dimension, Quart. Appl. Math., 1 (1990), 153-168. Zbl0703.35178MR1040239
15. FASANO, A., PRIMICERIO, M., HOWISON, S. - OCKENDON, J., On the singularities of one-dimensional Stefan problems with supercooling, in Mathematical Models for Phase Change Problems (J. F. RODRIGUEZ ed.), Int. Series Num. Math., 88, Birkhäuser (1989) pp. 215-226. Zbl0699.35266MR1038071
16. FASANO, A., PRIMICERIO, M. - LACEY, A. A., New results on some classical parabolic free boundary problems, Quart. Appl. Math., 38 (1981), 439-460. Zbl0468.35081MR614552
17. GÖTZ, I. G.- ZALTZMAN, B. B., Two phase Stefan problems with supercooling, SIAM J. Math. Anal., 26 (1995), 694-714. Zbl0826.35140MR1325910
18. GURTIN, M. E., Thermodynamics and supercritical Stefan equations with nucleation, Quart. Appl. Math., 52 (1994), 133-155. Zbl0809.35171MR1262324
19. HERRERO, M. A.- VELÁZQUEZ, J. J., Approaching an extinction point in one-dimensional semilinear equation with strong absorption, J. Math. Anal. Appl., 170 (1992), 353-381. Zbl0799.35111MR1188559
20. HERRERO, M. A.- VELÁZQUEZ, J. J. L., Singularity formation in the one-dimensional Stefan problem, EJAM, 7 (1996), 119-150. Zbl0855.35135MR1388108
21. HERRERO, M. A.- VELÁZQUEZ, J. J. L., On the melting of an ice ball, SIAM J. Math. Anal., 28 (1997), 1-32. Zbl0876.35137MR1427725
22. LACEY, A. A.- OCKENDON, J. R., Ill-posed free boundary problems, Control Cybernetics, 14 (1985), 275-296. Zbl0615.35079MR839524
23. SCHATZ, A., Free boundary problems of Stefan type with prescribed flux, J. Math. Anal. Appl., 28 (1969), 569-579. Zbl0271.35038MR267285
24. SHERMAN, B., A general one-phase Stefan problem, Quart. Appl. Math., 28 (1970), 377-382. Zbl0209.40502MR282082
25. VELÁZQUEZ, J. J. L., Cusp formation for the undercooled Stefan problem in two and three dimensions, EJAM, 8 (1997), 1-21. Zbl0876.35134MR1431410
26. VISINTIN, A., Stefan problem with a kinetic condition at the free boundary, Ann. Mat. Pura Appl., 146 (1987), 97-122. Zbl0643.35115MR916689
27. VISINTIN, A., Models of Phase Transitions, Birkhäuser, Boston (1996). Zbl0882.35004MR1423808

1. Ivan G. Götz, Mario Primicerio, Juan J. L. Velázquez, Asymptotic behaviour $t\to +0$ of the interface for the critical case of undercooled Stefan problem
2. Augusto Visintin, Transizioni di fase ed isteresi