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May  2009, 11(3): 741-784. doi: 10.3934/dcdsb.2009.11.741

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  February 2008 Revised  June 2008 Published  March 2009

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.
Keywords: dynamic transition theory, unified time-dependent Ginzburg-Landau equation., binary system, Cahn-Hilliard equation, phase transition dynamics, dynamic classification scheme of phase transitions.
Mathematics Subject Classification: Primary: 82B26, 82B30, 82C26, 82D15, 37L10, 35Q9.
Citation: Tian Ma, Shouhong Wang. Cahn-Hilliard equations and phase transition dynamics for binary systems. Discrete and Continuous Dynamical Systems - B, 2009, 11 (3) : 741-784. doi: 10.3934/dcdsb.2009.11.741
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