A Family of Nonlinear Fourth Order Equations of Gradient Flow Type

Global existence and long-time behavior of solutions to a family of nonlinear fourth order evolution equations on the d-dimensional euclidean space are studied.
Among them, for suitable values of the parameters we obtain a quantum drift diffusion model, and a thin film type equation.
These equations constitute gradient flows for the perturbed information functionals with respect to the L^2-Wasserstein metric.