Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical mass for a Patlak-Keller-Segel model with degenerate diffusion
  in higher dimensions   This paper is devoted to the analysis of non-negative solutions for a
generalisation of the classical parabolic-elliptic Patlak-Keller-Segel system
with $d\ge3$ and porous medium-like non-linear diffusion. Here, the non-linear
diffusion is chosen in such a way that its scaling and the one of the Poisson
term coincide. We exhibit that the qualitative behaviour of solutions is
decided by the initial mass of the system. Actually, there is a sharp critical
mass $M_c$ such that if $M \in (0,M_c]$ solutions exist globally in time,
whereas there are blowing-up solutions otherwise. We also show the existence of
self-similar solutions for $M \in (0,M_c)$. While characterising the eventual
infinite time blowing-up profile for $M=M_c$, we observe that the long time
asymptotics are much more complicated than in the classical Patlak-Keller-Segel
system in dimension two.

23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an