@article{b92057f1799c4102b1f2bf7f735aed79,
title = "A family of nonlinear fourth order equations of gradient flow type",
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 with respect to the L2-Wasserstein metric. The value of α ranges from α = 1/2, corresponding to a simplified quantum drift diffusion model, to α = 1, corresponding to a thin film type equation.",
keywords = "Entropy method, Fourth-order equations, Gradient flow, Nonlinear parabolic equations, References, Wasserstein distance",
author = "Matthes Daniel and McCann, {Robert J.} and Giuseppe Savar{\'e}",
note = "Funding Information: D. M. has been partially supported by the Deutsche Forschungsgemeinschaft, grant JU 359/7. He thanks the Department of Mathematics of the Universit{\`a} di Pavia, where part of this research has been carried out, for the kind hospitality. R. J. M. has been partially supported by US National Science Foundation grant DMS 0354729 and the Natural Sciences and Engineering Research Council of Canada grants RGPIN 217006-03 and -08. G. S. has been partially supported by MIUR-PRIN{\textquoteright}06 grant for the project “Variational methods in optimal mass transportation and in geometric measure theory”.",
year = "2009",
month = nov,
doi = "10.1080/03605300903296256",
language = "English",
volume = "34",
pages = "1352--1397",
journal = "Communications in Partial Differential Equations",
issn = "0360-5302",
publisher = "Taylor and Francis Ltd.",
number = "11",
}