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arXiv · 2010.04659

On nonnegative solutions for the Functionalized Cahn-Hilliard equation with degenerate mobility

Shibin Dai·Qiang Liu·Toai Luong·Keith Promislow
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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.

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Shibin Dai, Qiang Liu, Toai Luong, Keith Promislow. 2020-10-09. On nonnegative solutions for the Functionalized Cahn-Hilliard equation with degenerate mobility. https://doi.org/10.1016/j.rinam.2021.100195

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