Phase segregation dynamics in particle systems with long range interactions II: Interface motion

Giambattista Giacomin, Joel L. Lebowitz

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Abstract

We study properties of the solutions of a family of second-order integrodifferential equations, which describe the large scale dynamics of a class of microscopic phase segregation models with particle conserving dynamics. We first establish existence and uniqueness as well as some properties of the instantonic solutions. Then we concentrate on formal asymptotic (sharp interface) limits. We argue that the obtained interface evolution laws (a Stefan-like problem and the MullinsSekerka solidification model) coincide with the ones which can be obtained in the analogous limits from the Cahn-Hilliard equation, the fourth-order PDE which is the standard macroscopic model for phase segregation with one conservation law. Key words. nonlocal evolution equation, sharp interface limit, spinodal decomposition, Stefan problem, Mullins-Sekerka model, interacting particle systems, local mean field

Original languageEnglish (US)
Pages (from-to)1707-1729
Number of pages23
JournalSIAM Journal on Applied Mathematics
Volume58
Issue number6
DOIs
StatePublished - 1998

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

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