On the Cahn–Hilliard Equation with Degenerate Mobility

Abstract

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 $ \pm 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.