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
Keywords:
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)
http://dx.doi.org/10.1080/03605300903296256
Created from the Publication Database of the Vienna University of Technology.