Cahn-Hilliard equations  and phase transition dynamics  for binary systems

Tian Ma; Shouhong Wang

doi:10.3934/dcdsb.2009.11.741

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2009, Volume 11, Issue 3: 741-784. Doi: 10.3934/dcdsb.2009.11.741

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Cahn-Hilliard equations and phase transition dynamics for binary systems

Tian Ma^1, and
Shouhong Wang^2,

1.
Department of Mathematics, Sichuan University, Chengdu
2.
Department of Mathematics, Indiana University, Bloomington, IN 47405

Received: January 31, 2008

Revised: May 31, 2008

Published: April 2009

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Abstract

The process of phase separation of binary systems is described by the Cahn-Hilliard equation. The main objective of this article is to give a classification on the dynamic phase transitions for binary systems using either the classical Cahn-Hilliard equation or the Cahn-Hilliard equation coupled with entropy, leading to some interesting physical predictions. The analysis is based on dynamic transition theory for nonlinear systems and new classification scheme for dynamic transitions, developed recently by the authors.

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Mathematics Subject Classification: Primary: 82B26, 82B30, 82C26, 82D15, 37L10, 35Q99.

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