Global existence and asymptotic behavior for the radially symmetric case of a two-phase Stefan problem with interfacial energy

Journal of Mathematical Analysis and Applications

Volumn 211, Issue 1, 1997, Pages 1-29

  Scianna, Giuseppe ^a  

^a UNIVERSITY OF SIENA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; FUNCTIONS; INTERFACIAL ENERGY; PROBLEM SOLVING; SET THEORY; SURFACE TENSION;

GIBBS THOMSON LAW; PHASE CHANGE THEORY; TWO PHASE STEFAN PROBLEM;

MATHEMATICAL TECHNIQUES;

EID: 0031172964     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1997.5316     Document Type: Article

References (23)

1. 1. G. Caginalp, An analysis of a phase field model of a free boundary, Arch. Rational Mech. Anal. 92 (1986), 205-245.
2. 2. G. Caginalp and X. Chen, Phase field equations in the singular limit of sharp interface problems, in "IMA Volumes in Mathematics and Its Applications," Vol. 43, pp. 1-28, Springer-Verlag, New York/Berlin, 1990.
3. 3. G. Caginalp and P. C. Fife, Phase field methods for interfacial boundaries, Phys. Rev. B 34 (1986), 4940-4943.
4. 4. B. Chalmers, "Principles of solidification," Krieger, Hinton, NY, 1975.
5. 5. X. Chen and F. Reitich, Local existence and uniqueness of solutions of the Stefan problem with surface tension and kinetic undercooling, J. Math. Anal. Appl. 164 (1992), 350-362.
6. 6. A. Fasano and M. Primicerio, Free boundary problems for nonlinear parabolic equations with nonlinear free boundary conditions, J. Math. Anal. Appl. 72 (1979), 247-273.
7. 7. A. Friedman, "Partial Differential Equations of Parabolic Type," Prentice Hall, New York, 1964.
8. 8. A. Friedman and A. Tzavaras, Combustion in a porous medium, SIAM J. Math. Anal. 19 (1988).
9. 9. S. Fučic, O. John, and A. Kufner, "Function Spaces," Academia, Prague/Noordhoff, Leyden, 1977.
10. 10. M. E. Gurtin, On the two-phase Stefan Problem with interfacial energy and entropy, Arch. Rational Mech. Anal. 96 (1986), 199-241.
11. 11. O. A. Ladyženskaja, V. A. Solounikov and N. N. Ural'ceva, Linear and quasilinear equations of parabolic type, Trans. Amer. Math. Soc. Providence, R.I. (1968).
12. 12. L. D. Landau and E. M. Lifshitz, "Statistical Physics," Addison-Wesley, Reading, MA, 1968.
13. 13. S. Luckhaus, Solutions for the two-phase Stefan problem with the Gibbs-Thomson law for the melting temperature, European J. Appl. Math. 1 (1990), 101-111.
14. 14. S. Luckhaus and L. Modica, The Gibbs-Thomson relation within the gradient theory of phase transitions, Arch. Rational Mech. Anal. 107 (1989), 71-83.
15. 15. L. Modica, Gradient theory of phase transitions and minimal interface cryterion, Arch. Rational Mech. Anal. 98 (1987), 123-142.
16. 16. M. Primicerio, Problemi di diffusione a frontiera libera, Boll. Un. Mat. Ital. A (5) 18 (1981), 11-68.
17. 17. M. H. Protter and H. F. Weinberger, "Maximum Principles in Differential Equations," Springer-Verlag, New York/Berlin, 1984.
18. 18. J. C. Rogers, The Stefan problem with surface tension, in "Free Boundary Problems: Theory and Applications" (A. Fasano and M. Primicerio, Eds.), Pitman, Boston, 1983.
19. 19. L. I. Rubinstein, "The Stefan problem," Trans. Amer. Math. Soc. Providence, R.I. (1971).
20. 20. Chiang Li-Shang, Existence and differentiability of the solution of a two-phase Stefan problem for quasilinear parabolic equations, Acta Math. Sinica 15 (1965).
21. 21. A. Visintin, Stefan problem with surface tension, preprint, dell' Instituto di Analisi Numerica del C.N.R., Pavia 670, 1989.
22. 22. A. Visintin, Stefan problem with a kinetic condition at the free boundary, Ann. Mat. Pura Appl. (4) 146, (1987) 97-122.
23. 23. K. Yosida, "Functional Analysis," Springer-Verlag, New York/Berlin, 1965.