Ostwald ripening: The screening length revisited

Calculus of Variations and Partial Differential Equations

Volumn 13, Issue 1, 2001, Pages 33-68

  Niethammer, Barbara ^a   Otto, Felix ^a  

^a UNIVERSITY OF BONN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0013020764     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00009923     Document Type: Article

References (20)

1. N. Alikakos, P. Bates, and X. Chen. Convergence of the Cahn-Hilliard equation to the Hele-Shaw model. Arch. Rat. Mech. Anal., 128: 165-205, 1994.
2. N. Alikakos and G. Fusco. The equations of Ostwald ripening for dilute systems. J. Stat. Phys., 95, 5/6:851-866, 1999.
3. J. Carrand O. Penrose. Asymptotic behaviourin a simplified Lifshitz-Slyozov equation. Physica D, 124: 166-176, 1998.
4. D. Cioranescu and F. Murat. A strange term coming from nowhere. In A. Cherkaev, editor, Topics in the Mathematical Modelling of Composite Materials, pages 45-94. Birkhäuser, 1997.
5. L. C. Evans and R. F. Gariepy. Measure theory and fine properties of functions. CRC Press, 1992. Studies in Advanced Mathematics. Boca Raton.
6. J. S. Langer. An introduction to the kinetics of first-order phase transitions. Cambridge University Press, 1992. Solids far from equilibrium, C. Godrẽche (ed.).
7. I. M. Lifshitz and V. V. Slyozov. The kinetics of precipitation from supersaturated solid solutions. J. Phys. Chem. Solids, 19: 35-50, 1961.
8. M. Marder. Correlations and Ostwald ripening. Phys. Rev. A, 36: 858-874, 1987.
9. G. Dal Maso. An introduction to Γ-convergence. Birkhäuser, 1993. Progress in Nonlinear Differential Equations and their Applications. 8. Basel.
10. B. Niethammer. Derivation of the LSW-theory for Ostwald ripening by homogenization methods. Arch. Rat. Mech. Anal., 147, 2:119-178, 1999.
11. B. Niethammer and R. L. Pego. Non-self-similar behavior in the LSW theory of Ostwald ripening. J. Stat. Phys., 95, 5/6:867-902, 1999.
12. F. Otto. The geometry of dissipative evolution equations: the porous medium equation. Comm. Part. Diff. Eq. to appear.
13. F. Otto. Lubrication approximation with prescribed non-zero contact angle: an existence result. Comm. Part. Diff. Eq., 23: 2077-2164, 1998.
14. R. L. Pego. Front migration in the nonlinear Cahn-Hilliard equation. Proc. R. Soc. Lond. A, 422: 261-278, 1989.
15. p(0, T; B). Ann. Mat. Pura Appl., IV, Ser. 146: 65-96, 1987.
16. J. J. L. Velázquez. The Becker-Döring equations and the Lifshitz-Slyozov theory of coarsening. J. Stat. Phys., 92: 195-236, 1998.
17. J. J. L. Velázquez. On the effect of stochastic fluctuations in the dynamics of the Lifshitz-Slyozov-Wagner model. J. Stat. Phys., 2000. to appear.
18. P. W. Voorhees. The theory of Ostwald ripening. J. Stat. Phys., 38: 231-252, 1985.
19. P. W. Voorhees. Ostwald ripening of two-phase mixtures. Ann. Rev. Mater. Sc, 22: 197-215, 1992.
20. C. Wagner. Theorie der Alterung von Niederschlägen durch Umlösen. Z. Elektrochemie, 65: 581-594, 1961.