Shibin Dai, Qiang Liu, Toai Luong, Keith Promislow
Published 2020-10-09Version 1
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.
Monotonicity and symmetry of nonnegative solutions to $ -Δu=f(u) $ in half-planes and strips
Finite-strain poro-visco-elasticity with degenerate mobility
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