The equations of Ostwald ripening for dilute systems

Journal of Statistical Physics

Volumn 95, Issue 5-6, 1999, Pages 851-866

  Alikakos, Nicholas D ^a,b   Fusco, Giorgio ^c  

^a UNIVERSITY OF TENNESSEE   (United States)

^b UNIVERSITY OF ATHENS   (Greece)

^c NONE

Author keywords

Mullins sekerka; Ostwald ripening; Quasi static stefan; Stability of spherical shape

Indexed keywords

EID: 0033245857     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1004594131850     Document Type: Article

References (40)

1. 1. W. Ostwald, Z. Phys. Chem. 37:385 (1901).
2. 2. J. Rubinstein and P. Sternberg, IMA J. Appl. Math. 48:249-264 (1992).
3. 3. I. M. Lifschitz and V. V. Slyosov, J. Phys. Chem. Solids 19:35-50 (1961).
4. 4. C. Wagner, Z. Electrochem. 65:581-594 (1961).
5. 5. N. D. Alikakos and G. Fusco, preprint (1998).
6. 6. B. Niethammer, University of Bonn Technical Report 453 (1996).
7. 7. In progress.
8. 8. J. W. Cahn, Acta Metall. 9:795-801 (1961).
9. 9. J. W. Cahn and J. E. Billiard, J. Phys. Chem. 28:258-267 (1958).
10. 10. R. L. Pego, Proc. Roy. Soc. London, Ser. A 422:261-278 (1989).
11. 11. N. D. Alikakos, P. Bates, and X. Chen, Arch. Rat. Mech. Anal. 128:165-205 (1994).
12. 12. W. W. Mullins and R. F. Sekerka, J. Appl. Phys. 34:323-329 (1963).
13. 13. V. Alexiades, and A. D. Solomon, Mathematical Modeling of Melting and Freezing Processes, hemisphere Publishing Corporation (1993).
14. 14. X. Chen, X. Hong, and F. Yi, preprint (1997).
15. 15. X. Chen, Arch. Rational Mech. Anal. 123:117-151.
16. 16. P. Constantine and M. Pugh, Nonlinearity 6:393-415 (1993).
17. 17. J. Escher and G. Simonett, J.D.E. 143:267-292 (1998).
18. 18. X. Chen, Journal of Differential Geometry (to appear).
19. 19. J. Escher and G. Simonett, Advances in Differential Equations 2:619-642 (1997).
20. 20. N. D. Alikakos, J. Escher, G. Fusco, and G. Simonett (in progress).
21. 21. P. Fife, Dynamical Aspects of the Calm-Hilliard Equations (Barrett lectures, University of Tennessee, Spring 1991).
22. 22. G. Bellettini and G. Fusco, preprint (1997).
23. 23. N. D. Alikakos, P. W. Bates, X. Chen, and G. Fusco, preprint (1997).
24. 24. G. Huisken and S. T. Yau, Inventiones Mathematicae 281-311 (1996).
25. 25. R. Ye, Pacific Journal of Mathematics 147:381-396 (1991).
26. 26. G. Huisken, J. Reine Angew. Math. 382:35-48 (1987).
27. 27. C. Miranda, Lincei-Memorie Sc. Fisiche. esc. S.VIII VII, Sez. 1, 9 303-336 (1965).
28. 28. S. Agmon, A. Douglis, and L. Nirenberg, Comm. Pure Appl. Math. 12:623-727 (1959).
29. 29. G. Da Prato and P. Grisvard, Ann. Mat. Pura Appl. (4) 120:329-396 (1979).
30. 30. A. Lunardi, Analytic Semigroups and Optimal Regularity for Parabolic Problems (Birkhauser, Basel, 1995).
31. 31. H. Amann, Linear and Quasilinear Parabolic Problems, Vol. I (Birkhauser, Basel, 1995).
32. 32. S. B. Angenent, Proc. Roy. Soc. Edinburgh A 115:91-107 (1990).
33. 33. J. Zhu, X. Chen and T. X. Hou, J. Comput. Phys. 126 (1996).
34. 34. O. Penrose, J. L. Lebowitz, J. Murro, M. H. Kallos, and A. Sur, J. Stat. Phys. 19:243-267 (1978).
35. 35. M. Kalos, J. L. Lebowitz, O. Penrose, and A. Sur, J. Stat. Phys. 18:39-51 (1978).
36. 36. M. Soner.
37. 37. P. W. Voorhees, Journal of Statistical Physics 38:231-252 (1985); Ann. Rev. Mater. Sc. 22:197-215 (1992).
38. 37. P. W. Voorhees, Journal of Statistical Physics 38:231-252 (1985); Ann. Rev. Mater. Sc. 22:197-215 (1992).
39. 38. P. W. Voorhees and M. E. Glicksman, Theory, Acta Metall. 32:2001-2011 (1984).
40. 39. B. Niethammer and R. Pego, Non-Self-Similar Behavior in the LSW theory of Ostwald Ripening, preprint, 1998.