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From the Becker–Döring to the Lifshitz–Slyozov–Wagner Equations

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Abstract

Connections between two classical models of phase transitions, the Becker–Döring (BD) equations and the Lifshitz–Slyozov–Wagner (LSW) equations, are investigated. Homogeneous coefficients are considered and a scaling of the BD equations is introduced in the spirit of the previous works by Penrose and Collet, Goudon, Poupaud and Vasseur. Convergence of the solutions to these rescaled BD equations towards a solution to the LSW equations is shown. For general coefficients an approach in the spirit of numerical analysis allows to approximate the LSW equations by a sequence of BD equations. A new uniqueness result for the BD equations is also provided.

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Authors and Affiliations

  1. Mathématiques pour l'Industrie et la Physique, CNRS UMR 5640, [Université Paul Sabatier, Toulouse 3, 118 route de Narbonne, F-31062, Toulouse cedex 4, France

    Philippe Laurençot

  2. Laboratoire de Mathématiques Appliquées, Université de Versailles, Saint Quentin, 45 avenue des Etats-Unis, F-78035, Versailles, France

    Stéphane Mischler

  3. DMA, CNRS UMR 8553, Ecole Normale Supérieure, 45 rue d'Ulm, F-75230, Paris cedex 05, France

    Stéphane Mischler

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  1. Philippe Laurençot
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  2. Stéphane Mischler
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Laurençot, P., Mischler, S. From the Becker–Döring to the Lifshitz–Slyozov–Wagner Equations. Journal of Statistical Physics 106, 957–991 (2002). https://doi.org/10.1023/A:1014081619064

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