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Modelling phase transitions via Young measures

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  • We consider the elastic theory of single crystals at constant temperature where the free energy density depends on the local concentration of one or more species of particles in such a way that for a given local concentration vector certain lattice geometries (phases) are preferred. Furthermore we consider possible large deformations of the crystal lattice. After deriving the physical model, we indicate by means of a suitable implicite time discretization an existence result for measure-valued solutions that relies on a new existence theorem for Young measures in infinite settings. This article is an overview of [2].
    Mathematics Subject Classification: Primary: 74N15, 74N25, 74B20; Secondary: 35K55, 49J45, 28C20.


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