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Kinetic and Related Models (KRM)
 

The Lifschitz-Slyozov equation with space-diffusion of monomers
Pages: 325 - 355, Issue 2, June 2012

doi:10.3934/krm.2012.5.325      Abstract        References        Full text (593.1K)           Related Articles

Thierry Goudon - Project COFFEE, INRIA Sophia Antipolis Méditerranée Research Centre, & Labo. J. A. Dieudonné UMR 7351 CNRS{Université Nice Sophia Antipolis, Parc Valrose, 06108 Nice, France (email)
Frédéric Lagoutière - Laboratoire de Mathématiques, UMR 8628, CNRS-Université Paris-Sud 11, Bât. 425, Faculté des Sciences d'Orsay, Université Paris-Sud 11, F-91405 Orsay cedex,, France (email)
Léon M. Tine - Project-Team SIMPAF, INRIA Lille Nord Europe Research Centre, Park Plazza, 40 avenue Halley, F-59650 Villeneuve d'Ascq cedex, France (email)

1 H. Brézis, "Analyse Fonctionnelle. Théorie et Applications," Collection Mathématiques Appliquées pour la Maîtrise, Masson, Paris, 1983.       
2 J. A. Carrillo and T. Goudon, A numerical study on large-time asymptotics of the Lifschitz-Slyozov system, J. Scient. Comp., 18 (2003), 429-473.
3 L. Châun-Hoàn, "Étude de la Classe des Opérateurs $m-$Accrétifs de $L^1(\Omega)$ et Accrétifs dans $L^\infty(\Omega)$," Thèse de 3ème cycle, Université Paris VI, 1977.
4 M. K. Chen and P. W. Voorhees, The dynamics of transient Ostwald ripening, Modelling Simul. Mater. Sci. Eng., 1 (1993), 591-612.
5 E. A. Coddington and N. Levinson, "Theory of Ordinary Differential Equations," McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955.       
6 J.-F. Collet and T. Goudon, Lifschitz-Slyozov equations: The model with encounters, Transp. Theory Stat. Phys., 28 (1999), 545-573.       
7 J.-F. Collet and T. Goudon, On solutions of the Lifschitz-Slyozov model, Nonlinearity, 13 (2000), 1239-1262.       
8 J.-F. Collet, T. Goudon, F. Poupaud and A. Vasseur, The Becker-Döring system and its Lifschitz-Slyozov limit, SIAM J. Appl. Math., 62 (2002), 1488-1500.       
9 J.-F. Collet, T. Goudon and A. Vasseur, Some remarks on the large-time asymptotic of the Lifschitz-Slyozov equations, J. Stat. Phys., 108 (2002), 341-359.       
10 J. Conlon, On a diffusive version of the Lifschitz-Slyozov-Wagner equation, J. Nonlinear Sc., 20 (2010), 463-521.       
11 D. B. Dadyburjor and E. Ruckenstein, Kinetics of Ostwald ripening, J. Crystal Growth, 40 (1977), 279-290.
12 C. Dellacherie and P.-A. Meyer, "Probabilités et Potentiel," chapitres I à IV, Édition entièrement refondue, Publications de l'Institut de Mathématique de l'Université de Strasbourg, No. XV, Actualités Scientifiques et Industrielles, No. 1372, Hermann, Paris, 1975.       
13 R. Edwards, "Functional Analysis: Theory and Applications," Corrected reprint of the 1965 original, Dover Publications, Inc., New York, 1995.       
14 T. Goudon, "Intégration: Intégrale de Lebesgue et Introduction à l'Analyse Fonctionnelle," Ellipses, 2011.
15 S. Hariz and J.-F. Collet, A modified version of the Lifschitz-Slyozov model, Applied Math. Lett., 12 (1999), 81-85.       
16 M. Herrmann, B. Niethammer and J. J. L. Velázquez, Self-similar solutions for the LSW model with with encounters, J. Differential Equations, 247 (2009), 2282-2309.       
17 P. Laurençot, Weak solutions to the Lifschitz-Slyozov-Wagner equation, Indiana Univ. Math. J., 50 (2001), 1319-1346.       
18 P. Laurençot, The Lifschitz-Slyozov equation with encounters, Math. Models Methods Appl. Sci., 11 (2001), 731-748.       
19 P. Laurençot, The Lifschitz-Slyozov-Wagner equation with conserved total volume, SIAM J. Math. Anal., 34 (2002), 257-272.       
20 I. M. Lifschitz and L. Pitaevski, "Cinétique Physique," Cours de Physique Théorique, Vol. 10, L. Landau-I. Lifschitz, Mir, 1990.
21 I. M. Lifschitz and V. V. Slyozov, The kinetics of precipitation from supersaturated solid solutions, J. Phys. Chem. Solids, 19 (1961), 35-50.
22 B. Niethammer, A scaling limit of the Becker-Döring equations in the regime of small excess density, J. Nonlinear Sci., 14 (2004), 453-468.       
23 B. Niethammer and F. Otto, Ostwald ripening: The screening length revisited, Calc. Var. Partial Differential Equations, 13 (2001), 33-68.       
24 B. Niethammer and R. Pego, Non-self-similar behavior in the LSW theory of Ostwald ripening, J. Stat. Phys., 95 (1999), 867-902.       
25 B. Niethammer and R. Pego, On the initial-value problem in the Lifschitz-Slyozov-Wagner theory of Ostwald ripening, SIAM J. Math. Anal., 31 (2000), 467-485.       
26 B. Niethammer and R. Pego, The LSW model for domain coarsening: Asymptotic behavior for conserved total mass, J. Stat. Phys., 104 (2001), 1113-1144.       
27 B. Niethammer and R. L. Pego, Well-posedness for measure transport in a family of nonlocal domain coarsening models, Indiana Univ. Math. J., 54 (2005), 499-530.       
28 B. Niethammer and J. J. L. Velázquez, Global well-posedness for an inhomogeneous LSW-model in unbounded domains, Math. Ann., 328 (2004), 481-501.       
29 B. Niethammer and J. J. L. Velázquez, On screening induced fluctuations in Ostwald ripening, J. Stat. Phys., 130 (2008), 415-453.       
30 O. Penrose, The Becker-Döring equations at large times and their connection with the LSW theory of coarsening, J. Stat. Phys., 89 (1997), 305-320.       
31 T. Phillips, Trouble with Lifshitz, Slyozov and Wagner, Science News, NASA Science, 2003. Available from: http://www.nasa.gov/vision/earth/technologies/coarsening_prt.htm.
32 V. V. Sagalovich and V. V. Slyozov, Diffusive decomposition of solid solutions, Sov. Phys. Usp., 30 (1987), 23-44.
33 J. Simon, Compact sets in $L^p(0,T;B)$, Ann. Mat., Pura ed Appl. (4), 146 (1987), 65-96.       
34 L. M. Tiné, T. Goudon and F. Lagoutière, Simulations of the Lifschitz-Slyozov equations with coagulations terms: Finite volumes schemes and anti-diffusive strategies, preprint, 2011.
35 F. Trèves, "Topological Vector Spaces, Distributions and Kernels," Unabridged republication of the 1967 original, Dover Publications, Inc., Mineola, NY, 2006.       

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