Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The structure of the category of parabolic equations   We define here the category of partial differential equations. Special cases
of morphisms from an object (equation) are symmetries of the equation and
reductions of the equation by a symmetry groups, but there are many other
morphisms. We are mostly interested in a subcategory that arises from second
order parabolic equations on arbitrary manifolds. We introduce a certain
structure in this category enabling us to find the simplest representative of
every quotient object of the given object, and develop a special-purpose
language for description and study of structures of this kind. An example that
deals with nonlinear reaction-diffusion equation is discussed in more detail.

24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs