Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigorous derivation of population cross-diffusion systems from
  moderately interacting particle systems   Population cross-diffusion systems of Shigesada-Kawasaki-Teramoto type are
derived in a mean-field-type limit from stochastic, moderately interacting
many-particle systems for multiple population species in the whole space. The
diffusion term in the stochastic model depends nonlinearly on the interactions
between the individuals, and the drift term is the gradient of the
environmental potential. In the first step, the mean-field limit leads to an
intermediate nonlocal model. The local cross-diffusion system is derived in the
second step in a moderate scaling regime, when the interaction potentials
approach the Dirac delta distribution. The global existence of strong solutions
to the intermediate and the local diffusion systems is proved for sufficiently
small initial data. Furthermore, numerical simulations on the particle level
are presented.

35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an