Existence of solutions for a class of fourth order cross-diffusion systems of gradient flow type
Analysis of PDEs
2016-09-23 v1
Abstract
This article is concerned with the existence and the long time behavior of weak solutions to certain coupled systems of fourth-order degenerate parabolic equations of gradient flow type. The underlying metric is a Wasserstein-like transportation distance for vector-valued functions, with nonlinear mobilities in each component. Under the hypothesis of (flat) convexity of the driving free energy functional, weak solutions are constructed by means of the variational minimizing movement scheme for metric gradient flows. The essential regularity estimates are derived by variational methods.
Keywords
Cite
@article{arxiv.1609.06849,
title = {Existence of solutions for a class of fourth order cross-diffusion systems of gradient flow type},
author = {Daniel Matthes and Jonathan Zinsl},
journal= {arXiv preprint arXiv:1609.06849},
year = {2016}
}
Comments
28 pages, no figures. This research has been supported by the DFG Collaborative Research Center TRR 109 "Discretization in Geometry and Dynamics"