  In this paper, we establish a novel approach to proving existence of
non-negative weak solutions for degenerate parabolic equations of fourth order,
like the Cahn-Hilliard and certain thin film equations. The considered
evolution equations are in the form of a gradient flow for a perturbed
Dirichlet energy with respect to a Wasserstein-like transport metric, and weak
solutions are obtained as curves of maximal slope. Our main assumption is that
the mobility of the particles is a concave function of their spatial density. A
qualitative difference of our approach to previous ones is that essential
properties of the solution - non-negativity, conservation of the total mass and
dissipation of the energy - are automatically guaranteed by the construction
from minimizing movements in the energy landscape.

Analysis of PDEs