An existence result for the Cahn–Hilliard equation with a concentration dependent diffusional mobility is presented. In particular, the mobility is allowed to vanish when the scaled concentration takes the values ± 1, and it is shown that the solution is bounded by 1 in magnitude. Finally, applications of our method to other degenerate fourth-order parabolic equations are discussed.
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Elliott et al. (1996) studied this question.
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