Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Traveling plateaus for a hyperbolic Keller-Segel system with attraction
  and repulsion: existence and branching instabilities   How can repulsive and attractive forces, acting on a conservative system,
create stable traveling patterns or branching instabilities? We have proposed
to study this question in the framework of the hyperbolic Keller-Segel system
with logistic sensitivity. This is a model system motivated by experiments on
cell communities auto-organization, a field which is also called socio-biology.
We continue earlier modeling work, where we have shown numerically that
branching patterns arise for this system and we have analyzed this instability
by formal asymptotics for small diffusivity of the chemo-repellent. Here we are
interested in the more general situation, where the diffusivities of both the
chemo-attractant and the chemo-repellent are positive. To do so, we develop an
appropriate functional analysis framework. We apply our method to two cases.
Firstly we analyze steady states. Secondly we analyze traveling waves when
neglecting the degradation coefficient of the chemo-repellent; the unique wave
speed appears through a singularity cancelation which is the main theoretical
difficulty. This shows that in different situations the cell density takes the
shape of a plateau. The existence of steady states and traveling plateaus are a
symptom of how rich the system is and why branching instabilities can occur.
Numerical tests show that large plateaus may split into smaller ones, which
remain stable.

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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: econ