A mathematical model and an existence theory for non-isothermal phase separation

Abstract

We present a mathematical model for non-isothermal phase separation in binary systems. The model is constructed within the Landau-Ginzburg theory of phase transitions and non-equilibrium thermodynamics. It consists of a system of nonlinear parabolic differential equations for the order parameter and the energy as conserved quantities. The model is conformable with the first principles of thermodynamics. Besides a description of the model we study the stability of stationary solutions, and give a survey of the existence theory for the system of governing differential equations.Ams-Classification35K5535B40