The Lifshitz-Slyozov equation with encounters

Mathematical Models and Methods in Applied Sciences

Volumn 11, Issue 4, 2001, Pages 731-748

  Laurençot, Philippe ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035614951     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202501001070     Document Type: Article

References (19)

1. D. J. Aldous, Deterministic and stochastic models for coalescence (aggregation, coagulation): a review of the mean-field theory for probabilists, Bernoulli 5 (1999) 3-48.
2. J. Carr and O. Penrose, Asymptotic behaviour of solutions to a simplified Lifshitz-Slyozov equation, Phys. D124 (1998) 166-176.
3. J. F. Collet and T. Goudon, On solutions of the Lifshitz-Slyozov model, Nonlinearity 13 (2000) 1239-1262.
4. J. F. Collet and T. Goudon, Lifshitz-Slyozov equations: the model with encounters, Transport Theory Statist. Phys. 28 (1999) 545-573.
5. C. Dellacherie and P. A. Meyer, Probabilités et Potentiel (Hermann, 1975), Chaps. I and IV.
6. R. J. DiPerna and P. L. Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math. 98 (1989) 511-547.
7. P. B. Dubovskiǐ, Mathematical Theory of Coagulation, Lecture Notes Ser., Vol. 23 (Seoul Nat. Univ., 1994).
8. P. B. Dubovskiǐ and I. W. Stewart, Existence, uniqueness and mass conservation for the coagulation-fragmentation equation, Math. Methods Appl. Sci. 19 (1996) 571-591.
9. Ph. Laurençot, Weak solutions to the Lifshitz-Slyozov-Wagner equation, Indiana Univ. Math. J., to appear.
10. ème cycle, Université de Paris VI (1977).
11. I. M. Lifshitz and V. V. Slyozov, The kinetics of precipitation from supersaturated solid solutions, J. Phys. Chem. Solids 19 (1961) 35-50.
12. B. Niethammer and R. L. Pego, On the initial-value problem in the Lifshitz-Slyozov-Wagner theory of Ostwald ripening, SIAM J. Math. Anal. 31 (2000) 467-485.
13. B. Niethammer and R. L. Pego, Non-self-similar behavior in the LSW theory of Ostwald ripening, J. Statist. Phys. 95 (1999) 867-902.
14. L. Ratke, Simultaneous coarsening of dispersions by growth and coagulation, J. Colloid Interface Sci. 119 (1987) 391-397.
15. V. V. Slezov and V. V. Sagalovich, Diffusive decomposition of solid solutions, Sov. Phys. Usp. 30 (1987) 23-45.
16. I. W. Stewart, A global existence theorem for the general coagulation-fragmentation equation with unbounded kernels, Math. Methods Appl. Sci. 11 (1989) 627-648.
17. I. W. Stewart, Density conservation for a coagulation equation, Z. Angew. Math. Phys. 42 (1991) 746-756.
18. I. I. Vrabie, Compactness Methods for Nonlinear Evolutions, Pitman Monogr. Surveys Pure Appl. Math., Vol. 75 (Longman, 1995), 2nd edition.
19. C. Wagner, Theorie der Alterung von Niederschlägen durch Umlösen (Ostwald-Reifung), Z. Elektrochem. 65 (1961) 581-591.