Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mass threshold for infinite-time blowup in a chemotaxis model with
  splitted population   We study the chemotaxis model $\partial$ t u = div($\nabla$u -- u$\nabla$w) +
$\theta$v -- u in (0, $\infty$) x $\Omega$, $\partial$ t v = u -- $\theta$v in
(0, $\infty$) x $\Omega$, $\partial$ t w = D$\Delta$w -- $\alpha$w + v in (0,
$\infty$) x $\Omega$, with no-flux boundary conditions in a bounded and smooth
domain $\Omega$ $\subset$ R 2 , where u and v represent the densities of
subpopulations of moving and static individuals of some species, respectively,
and w the concentration of a chemoattractant. We prove that, in an appropriate
functional setting, all solutions exist globally in time. Moreover, we
establish the existence of a critical mass M c > 0 of the whole population u +
v such that, for M $\in$ (0, M c), any solution is bounded, while, for almost
all M > M c , there exist solutions blowing up in infinite time. The building
block of the analysis is the construction of a Liapunov functional. As far as
we know, this is the first result of this kind when the mass conservation
includes the two subpopulations and not only the moving one.

18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an