Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of solutions for a class of fourth order cross-diffusion
  systems of gradient flow type   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.

4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg