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

The Functionalized Cahn–Hilliard equation has been proposed as a model for the interfacial energy of phase-separated mixtures amphiphilic molecules. We study existence nonnegative weak solutions gradient flow subject to degenerate mobility M(u) that is zero u≤0. Assuming initial data u0(x) positive, we construct solution limit corresponding non-degenerate mobilities and verify it satisfies an dissipation inequality. Our approach combination Galerkin approximation, estimates, convergence methods.