Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On two-signed solutions to a second order semi-linear parabolic partial
  differential equation with non-Lipschitz nonlinearity   In this paper, we establish the existence of a 1-parameter family of
spatially inhomogeneous radially symmetric classical self-similar solutions to
a Cauchy problem for a semi-linear parabolic PDE with non-Lipschitz
nonlinearity and trivial initial data. Specifically we establish well-posedness
for an associated initial value problem for a singular two-dimensional
non-autonomous dynamical system with non-Lipschitz nonlinearity. Additionally,
we establish that solutions to the initial value problem converge algebraically
to the origin and oscillate as $\eta\to \infty$.

7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin