Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global existence and steady states of a two competing species
  Keller-Segel chemotaxis model   We study an one{dimensional quasilinear system proposed by J. Tello and M.
Winkler [19] which models the population dynamics of two competing species
attracted by the same chemical. The kinetics terms of the interacting species
are chosen to be the Lotka{Volterra type. We prove the existence of global
bounded and classical solutions for all chemoattraction rates. Under
homogeneous Neumann boundary conditions, we establish the existence of
nonconstant steady states by local bifurcation theory. The stability of the
bifurcating solutions is also obtained when the diffusivity of both species is
large. Finally, we perform extensive numerical studies to demonstrate the
formation of stable positive steady states with various interesting spatial
structures.

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The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas