Derivation of the LSW-theory for Ostwald ripening by homogenization methods

Archive for Rational Mechanics and Analysis

Volumn 147, Issue 2, 1999, Pages 119-178

  Niethammer, Barbara ^a  

^a UNIVERSITY OF BONN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033426406     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050050147     Document Type: Article

References (42)

1. H.W. ALT, Lineare Funktionalanalysis, Springer, Berlin, 1985.
2. L. C. BROWN, A new examination of classical coarsening theory, Acta Metall., 37 (1989) 71-77.
3. C. W. BEENAKKER & J. ROSS, Theory of Ostwald ripening for open systems, J. Chem. Phys., 83 (1985) 4710-4714.
4. G. CAGINALP, Length scales in phase transition models: phase field, Cahn-Hilliard and blow-up problems, Pattern Formation: Symmetry Methods and Applications, Fields Inst. Comm., eds. J. CHADAM & W. LANGFORD, Amer. Math. Soc., 1994.
5. J. CARR & R. PEGO, Self similarity in a coarsening model in one dimension, Proc. Roy. Soc. Lond. A, 436 (1992) 569-583.
6. D. CIORANESCU & F. MURAT, Un terme étrange venu d'ailleurs I & II, Nonlinear partial differential equations and their applications, Collège de France Seminars II & III, ed. by H. BREZIS & J.-L. LIONS, Res. Notes in Mat., 60 & 70, Pitman, London (1982) 98-138, 154-178.
7. E. A. COUTSIAS & J. C. NEU, The aging of nuclei in a binary mixture, Physica D, 12 (1984) 295-302.
8. B. DACOROGNA, Weak Continuity and Weak Lower Semicontinuity of Non-Linear Functionals, Lect. Notes in Math. 92, Springer, Berlin, 1982.
9. Y. ENOMOTO & T. KAWASAKI, Acta Metall. Mater., 38 (1989), 1399-1413.
10. L. C. EVANS, Weak Convergence Methods for Nolinear Partial Differential Equations (CBMS Reg. Conf. Series, vol 74, Amer. Math. Soc., 1990).
11. D. J. EYRE, Coarsening dynamics for solutions of the Cahn-Hilliard equation in one space dimension, preprint (1992).
12. A. FRIEDMAN & B. OU, A model of crystal precipitation, J. Math. Anal. Appl., 137 (1989) 550-575.
13. A. FRIEDMAN, B. OU & D. ROSS, Crystal Precipitation with Discrete Initial Data, J. Math. Anal. Appl., 137 (1989) 576-590.
14. A. FRIEDMAN, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, 1964.
15. R. FIGARI, G. PAPANICOLAU & J. RUBINSTEIN, Remarks on the point interaction approximation, Hydrodynamic Behavior and Interacting Particle Systems, Springer, 1986, 45-55.
16. E. GIUSTI, Minimal Surfaces and Functions of Bounded Variation, Birkhäuser, Stuttgart, 1984.
17. D. GILBARG & N. S. TRUDINGER, Elliptic Partial Differential Equations of Second Order, 2nd edn., Springer, Berlin, 1983.
18. M. GURTIN, On the two-phase Stefan problem with interfacial energy and entropy, Arch. Rational Mech. Anal., 96 (1986) 199-241.
19. M. HILLERT, O. HUNDERI, N. RYUM & T. SAETRE, A comment on the Lifshitz-Slyozov-Wagner theory of particle coarsening, Scr. Metall., 23 (1989) 1979-1982.
20. J. J. HOYT, On the steady-state particle size distributions during coarsening, Scr. Metall., 24 (1990) 163-166.
21. I. M. LIFSHITZ & V. V. SLYOZOV, The kinetics of precipitation from supersaturated solid solutions, J. Phys. Chem. Solids, 19 (1961) 35-50.
22. O. A. LADYŽENSKAJA, V.A. SOLONNIKOV & N.N. URALTSEVA, Linear and Quasilinear Equations of parabolic Type, Amer. Math. Soc., Providence, 1968.
23. S. LUCKHAUS, Solutions for the two-phase Stefan problem with the Gibbs-Thomson law for the melting temperature, Euro. J. Appl. Math., 1 (1990) 101-111.
24. M. MARDER, Correlations and Droplet Growth, Phys. Rev. Lett., 55 (1985) 2953-2956.
25. M. MARDER, Correlations and Ostwald ripening, Phys. Rev. A, 36 (1987) 858-874.
26. J. A. MARQUSEE & J. ROSS, Kinetics of phase transitions: Theory of Ostwald ripening, J. Chem. Phys., 79 (1983) 373-378.
27. J. A. MARQUSEE & J. ROSS, Theory of Ostwald ripening: Competitive growth and its dependence on volume fraction, J. Chem. Phys., 80 (1984) 536-543.
28. J. C. NEU, unpublished note (1993).
29. B. NIETHAMMER, Approximation of Coarsening Models by Homogenization of a Stefan Problem, Ph.D. thesis, University of Bonn, available as Preprint SFB 256, No. 453, (1996).
30. B. NIETHAMMER, Kinetic undercooling in the mean-field theory for Ostwald ripening, University of Bonn, SFB256 report No. 549, (1997).
31. W. OSTWALD, Z. Phys. Chem., 37 (1901) 385.
32. J. RUBINSTEIN, Ph.D. thesis, NYU, (1985).
33. W. RUDIN, Real and Complex Analysis, 3rd edn., Mc Graw-Hill, New York, 1986.
34. B. E. STOTH, Convergence of the two-phase Stefan problem to the one-phase problem, Quart. Appl. Math., 55 (1997) 113-126.
35. L. TARTAR, Compensated Compactness and applications to partial differential equations, In Nonlinear Analysis and Mechanics, Heriot-Watt Symposium, Vol. 4, ed. R. KNOPS, Pitman Research Notes in Math. 39 (1979) 139-212.
36. L. TARTAR, Compensated Compactness and applications to partial differential equations, In Nonlinear Analysis and Mechanics, Heriot-Watt Symposium, Vol. 4, ed. R. KNOPS, Pitman Research Notes in Math. 39 (1979) 139-212.
37. M. TOKUYAMA & K. KAWASAKI, Statistical-mechanical theory of coarsening of spherical droplets, Physica A, 123 (1984) 386-411.
38. A. VISINTIN, Stefan Problem with surface tension, Mathematical Models for Phase Change Problems, ed. J. F. RODRIGUES, Birkhäuser, Stuttgart, 1988.
39. P.W. VOORHEES, The Theory of Ostwald ripening, J. Stat. Phys., 38 (1985) 231-252.
40. P. W. VOORHEES, Ostwald ripening of two-phase mixtures, Ann. Rev. Mater. Sci., 22 (1992) 197-215.
41. P. W. VOORHEES & M. E. GLICKSMAN, Solution to the multi-particle diffusion problem with applications to Ostwald ripening - I. Theory, Acta Metall., 32 (1984) 2001-2011.
42. C. WAGNER, Theorie der Alterung von Niederschlägen durch Umlösen, Z. Elektrochem., 65 (1961) 581-594.