We prove existence in one space dimension of weak solutions for the Neumann problem for a degenerate parabolic system consisting of a fourth-order and a second-order equation with singular lower-order terms. This system arises in the description of phase separation and ordering in binary alloys.
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Roberta Dal Passo, Amy Novick-Cohen, Lorenzo Giacomelli, Existence for an Allen-Cahn/Cahn-Hilliard system with degenerate mobility. Interfaces Free Bound. 1 (1999), no. 2, pp. 199–226DOI 10.4171/IFB/9