Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vast multiplicity of very singular self-similar solutions of a
  semilinear higher-order diffusion equation with time-dependent absorption   It is shown that a fourth-order semilinear parabolic equation with
time-dependent absorption admit a vast multiplicity of the so-called very
singular self-similar solutions (VSSs), which can bifurcate from some
eigenfunctions of the linearized operators and also are generated by branching
from other critical point. For the second-order semilinear heat equations, such
VSSs have been known since the beginning of the 1980s and were constructed in
papers by Brezis, Friedman, Galaktionov, Kyrdyumov, Samarskii, Peletier, Kamin,
Veron, and many others.

21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom