Publications in Scientific Journals:

D. Matthes, R.J. McCann, G. Savaré:
"A family of fourth order equations of gradient flow type";
Communications in Partial Differential Equations, 34 (2009), 11; 1352 - 1397.

English abstract:
Global existence and long-time behavior of solutions to a family of nonlinear fourth order evolution equations on Rd are studied. These equations constitute gradient flows for the perturbed information functionals F[u] = \int |\grad u^\alpha|^2 + |x|^2 u dx with respect to the L2-Wasserstein metric. The value of \alpha ranges from 1/2, corresponding to a simplified quantum drift diffusion model, to 1, corresponding to a thin film type equation.

German abstract:
siehe engl. Abstract

Entropy method; Fourth-order equations; Gradient flow; Nonlinear parabolic equations; Wasserstein distance

"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)

Created from the Publication Database of the Vienna University of Technology.