Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Well-posedness of a Parabolic-hyperbolic Keller-Segel System in the
  Sobolev Space Framework   We study the global strong solutions to a 3-dimensional parabolic-hyperbolic
Keller-Segel model with initial data close to a stable equilibrium with
perturbations belonging to $L^2(\mathbb R^3)\times H^1(\mathbb{R}^3)$. We
obtain global well-posedness and decay property. Furthermore, if the mean value
of initial cell density is smaller than a suitabale constant, then the chemical
concentration decays exponentially to zero as $t$ goes to infinity. Proofs of
the main results are based on an application of Fourier analysis method to
uniform estimates for a linearized parabolic-hyperbolic system and also based
on the smoothing effect of the cell density as well as the damping effect of
the chemical concentration.

34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga