Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: No critical nonlinear diffusion in 1D quasilinear fully parabolic
  chemotaxis system   This paper deals with the fully parabolic 1d chemotaxis system with diffusion
1/(1 + u). We prove that the above mentioned nonlinearity, despite being a
natural candidate, is not critical. It means that for such a diffusion any
initial condition, independently on the magnitude of mass, generates
global-in-time solution. In view of our theorem one sees that one-dimensional
Keller- Segel system is essentially different than its higher-dimensional
versions. In order to prove our theorem we establish a new Lyapunov-like
functional associated to the system. The information we gain from our new
functional (together with some estimates based on the well-known old Lyapunov
functional) turns out to be rich enough to establish global existence for the
initial-boundary value problem.

8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn