Variational Formulation of Phase Transitions with Glass Formation

Visintin, Augusto

Bollettino della Unione matematica italiana, Série 9, Tome 6 (2013) no. 1, pp. 75-111.

Résumé

In the framework of the theory of nonequilibrium thermodynamics, phase transitions with glass formation in binary alloys are here modelled as a multi-non-linear 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 $\gamma$-convergence. This latter issue is here dealt with in some simpler settings.

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