Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Long time existence of Smooth solution for the porous medium equation in
  a bounded domain
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio