Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A cross-diffusion system derived from a Fokker-Planck equation with
  partial averaging   A cross-diffusion system for two compoments with a Laplacian structure is
analyzed on the multi-dimensional torus. This system, which was recently
suggested by P.-L. Lions, is formally derived from a Fokker-Planck equation for
the probability density associated to a multi-dimensional It\={o} process,
assuming that the diffusion coefficients depend on partial averages of the
probability density with exponential weights. A main feature is that the
diffusion matrix of the limiting cross-diffusion system is generally neither
symmetric nor positive definite, but its structure allows for the use of
entropy methods. The global-in-time existence of positive weak solutions is
proved and, under a simplifying assumption, the large-time asymptotics is
investigated.

11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs