Phase Segregation Dynamics In Particle Systems with Long Range Interactions II: Interface motion

Details Phase Segregation Dynamics In Particle Systems with Long Range Interactions II: Interface motion Phase Segregation Dynamics In Particle Systems with Long Range Interactions II: Interface motion

1997-04-29

arxiv.org/abs/patt-sol/9705001v1

Nonlinear Sciences

Pattern Formation and Solitons

amstex with macros for numbering the formulas, tex twice, 24 pages

Scientific paper

We study properties of the solutions of a family of second order integro-differential 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 Mullins-Sekerka 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.

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