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Journal of Statistical Physics

, Volume 106, Issue 5–6, pp 957–991 | Cite as

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

  • Philippe Laurençot
  • Stéphane Mischler
Article

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.

asymptotics Becker–Döring equations kinetics of phase transitions Lifshitz–Slyozov–Wagner equation uniqueness 

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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • Philippe Laurençot
    • 1
  • Stéphane Mischler
    • 2
    • 3
  1. 1.Mathématiques pour l'Industrie et la Physique, CNRS UMR 5640[Université Paul SabatierToulouse cedex 4France
  2. 2.Laboratoire de Mathématiques AppliquéesUniversité de VersaillesVersaillesFrance
  3. 3.DMA, CNRS UMR 8553Ecole Normale SupérieureParis cedex 05France

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