Mathematical Sciences: Selection Criteria and Metastable States for Phase Transitions in Fluids and Solids

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This research program is concerned with two related projects. One is the selection of equilibrium states of a three dimensional, nonlinearly elastic body undergoing a phase transformation. The selection criterion involves a singular perturbation problem for a nonconvex functional in a variational formulation. The second is the study of the long time behavior of the solutions of the Cahn-Hilliard equation which models the phase-separation of binary alloys and polymer mixtures that have been rapidly cooled. The results from these two projects are expected to have significant impact on engineering mechanics.