Variational formulation of phase transitions with glass formation

Abstract

In the framework of the theory of nonequilibrium thermodynamics, phase transitions with glass formation in binary alloys are here modeled as a multi-nonlinear system of PDEs. A weak formulation is provided for an initial- and boundary-value problem, and existence of a solution is studied. This model is then reformulated as a minimization problem, on the basis of a theory that was pioneered by Fitzpatrick [MR 1009594]. This provides a tool for the analysis of compactness and structural stability of the dependence of the solution(s) on data and operators, via De Giorgi’s notion of Γ-convergence. This latter issue is here dealt with in some simpler settings.