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D. Matthes, R.J. McCann, G. Savaré:
"A family of nonlinear fourth order equations of gradient flow type";
in: "ASC Report 11/2009", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2009, ISBN: 978-3-902627-02-5.

Global existence and long-time behavior of solutions to a family
of nonlinear fourth order evolution equations on R^d are studied.
These equations constitute gradient flows for the perturbed information
functionals J(u) = 1/(2p) \int | D(w^p) |^2 + L/2 \int |x|^2 u with respect to
the L2-Wasserstein metric. The value of the parameter p ranges from
p=1/2, corresponding to a simplified quantum drift diffusion model,
to p=1, corresponding to a thin film type equation.

fourth order equations, gradient flows, Wasserstein metric, entropy method, lubrication equations

http://www.asc.tuwien.ac.at/preprint/2009/asc11x2009.pdf