Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the global solvability of porous media equations with general
  (spatially dependent) advection terms   We show that advection-diffusion equations with porous media type diffusion
and integrable initial data are globally solvable under very mild conditions.
Some generalizations and related results are also given.

17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn