Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Blow-up, concentration phenomenon and global existence for the
  Keller-Segel model in high dimension   This paper is devoted to the analysis of the classical Keller-Segel system
over $\mathbb{R}^d$, $d\geq 3$. We describe as much as possible the dynamics of
the system characterized by various criteria, both in the parabolic-elliptic
case and in the fully parabolic case. The main results when dealing with the
parabolic-elliptic case are: local existence without smallness assumption on
the initial density, global existence under an improved smallness condition and
comparison of blow-up criteria. A new concentration phenomenon criteria for the
fully parabolic case is also given. The analysis is completed by a
visualization tool based on the reduction of the parabolic-elliptic system to a
finite-dimensional dynamical system of gradient flow type, sharing features
similar to the infinite-dimensional system.

36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph