Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Compactness Theorem for Homogenization of Parabolic Partial
  Differential Equations   In order to have a better description of homogenization for parabolic partial
differential equations with periodic coefficients, we define the notion of
parametric two-scale convergence. A compactness theorem is proved to justify
this notion.

31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
19
The categories of this paper are: eess
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph