Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pattern formation in a Keller-Segel chemotaxis model with logistic
  growth   In this paper we investigate pattern formation in Keller--Segel chemotaxis
models over a multi--dimensional bounded domain subject to homogeneous Neumann
boundary conditions. It is shown that the positive homogeneous steady state
loses its stability as chemoattraction rate $\chi$ increases. Then using
Crandall--Rabinowitz local theory with $\chi$ being the bifurcation parameter,
we obtain the existence of nonhomogeneous steady states of the system which
bifurcate from this homogeneous steady state. Stability of the bifurcating
solutions is also established through rigorous and detailed calculations. Our
results provide a selection mechanism of stable wavemode which states that the
only stable bifurcation branch must have a wavemode number that minimizes the
bifurcation value. Finally we perform extensive numerical simulations on the
formation of stable steady states with striking structures such as boundary
spikes, interior spikes, stripes, etc. These nontrivial patterns can model
cellular aggregation that develop through chemotactic movements in biological
systems.

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The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat