Abstract
We prove existence of solutions to the initial-boundary value problem for the quasistationary phase field equations with a multidimensional order parameter. We show that these solutions satisfy the entropy maximum principle and the entropy production minimum principle. We obtain a new selection theorem for differential inclusion with multifunctions generated by weak differentials of marginal functions.
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Plotnikov, P.I., Klepacheva, A.V. The Phase Field Equations and Gradient Flows of Marginal Functions. Siberian Mathematical Journal 42, 551–567 (2001). https://doi.org/10.1023/A:1010431411758
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DOI: https://doi.org/10.1023/A:1010431411758