Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic Behavior for Critical Patlak-Keller-Segel model and an
  Repulsive-Attractive Aggregation Equation   In this paper we study the long time asymptotic behavior for a class of
diffusion-aggregation equations. Most results except the ones in Section 3.3
concern radial solutions. The main tools used in the paper are
maximum-principle type arguments on mass concentration of solutions, as well as
energy method. For the Patlak-Keller-Segel problem with critical power
$m=2-2/d$, we prove that all radial solutions with critical mass would converge
to a family of stationary solutions, while all radial solutions with
subcritical mass converge to a self-similar dissipating solution algebraically
fast. For non-radial solutions, we obtain convergence towards the self-similar
dissipating solution when the mass is sufficiently small. We also apply the
mass comparison method to another aggregation model with repulsive-attractive
interaction, and prove that radial solutions converge to the stationary
solution exponentially fast.

15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat