# American Institute of Mathematical Sciences

August  2005, 5(3): 753-768. doi: 10.3934/dcdsb.2005.5.753

## Nonisothermal phase separation based on a microforce balance

 1 Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 6086, SP2MI, 86962 Chasseneuil Futuroscope Cedex, France 2 Università degli Studi di Pavia, Dipartimento di Matematica "F. Casorati", Via Ferrata 1, 27100 Pavia, Italy

Received  June 2004 Revised  March 2005 Published  May 2005

Our aim in this article is to derive models for nonisothermal phase separation. Starting from the two fundamental laws of thermodynamics, we consider the approach of Gurtin, based on a balance law for microforces, to derive nonisothermal Cahn-Hilliard type equations. These equations extend previous models derived by Alt and Pawłow based on an entropy principle to nonisotropic materials and to systems that are far from equilibrium. We also extend this approach to the Ginzburg-Landau (Allen-Cahn) equation, for which we recover, as particular cases, some models obtained by Frémond with a physically different approach.
Citation: Alain Miranville, Giulio Schimperna. Nonisothermal phase separation based on a microforce balance. Discrete & Continuous Dynamical Systems - B, 2005, 5 (3) : 753-768. doi: 10.3934/dcdsb.2005.5.753
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