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On nonnegative solutions for the Functionalized Cahn-Hilliard equation with degenerate mobility (2010.04659v1)
Published 9 Oct 2020 in math.AP
Abstract: The Functionalized Cahn-Hilliard equation has been proposed as a model for the interfacial energy of phase-separated mixtures of amphiphilic molecules. We study the existence of a nonnegative weak solutions of a gradient flow of the Functionalized Cahn-Hilliard equation subject to a degenerate mobility M(u) that is zero for u<=0. Assuming the initial data u0(x) is positive, we construct a weak solution as the limit of solutions corresponding to nondegenerate mobilities and verify that it satisfies an energy dissipation inequality.