Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Preliminarily group classification of a class of 2D nonlinear heat
  equations   A preliminary group classification of the class 2D nonlinear heat equations
$u_t=f(x,y,u,u_x,u_y)(u_{xx}+u_{yy})$, where $f$ is arbitrary smooth function
of the variables $x,y,u,u_x$ and $u_y$ using Lie method, is given. The paper is
one of the few applications of an algebraic approach to the problem of group
classification: the method of preliminary group classification.

34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin