Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence of a Finite Volume Scheme for a System of Interacting
  Species with Cross-Diffusion   In this work we present the convergence of a positivity preserving
semi-discrete finite volume scheme for a coupled system of two non-local
partial differential equations with cross-diffusion. The key to proving the
convergence result is to establish positivity in order to obtain a discrete
energy estimate to obtain compactness. We numerically observe the convergence
to reference solutions with a first order accuracy in space. Moreover we
recover segregated stationary states in spite of the regularising effect of the
self-diffusion. However, if the self-diffusion or the cross-diffusion is strong
enough, mixing occurs while both densities remain continuous.

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The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an