Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the finite time blow-up for filtration problems with nonlinear
  reaction   We present results for finite time blow-up for filtration problems with
nonlinear reaction under appropriate assumptions on the nonlinearities and the
initial data. In particular, we prove first finite time blow up of solutions
subject to sufficiently large initial data provided that the reaction term
"overpowers" the nonlinear diffusion in a certain sense. Secondly, under
related assumptions on the nonlinearities, we show that initial data above
positive stationary state solutions will always lead to finite time blow up.

9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th