Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a cross-diffusion segregation problem arising from a model of
  interacting particles   We prove the existence of solutions of a cross-diffusion parabolic population
problem. The system of partial differential equations is deduced as the limit
equations satisfied by the densities corresponding to an interacting particles
system modeled by stochastic differential equations. According to the values of
the diffusion parameters related to the intra and inter-population repulsion
intensities, the system may be classified in terms of an associated matrix. For
proving the existence of solutions when the matrix is positive definite, we use
a fully discrete finite element approximation in a general functional setting.
If the matrix is only positive semi-definite, we use a regularization technique
based on a related cross-diffusion model under more restrictive functional
assumptions. We provide some numerical experiments demonstrating the weak and
strong segregation effects corresponding to both types of matrices.

23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg