Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Threshold phenomena for symmetric decreasing solutions of
  reaction-diffusion equations   We study the long time behavior of solutions of the Cauchy problem for
nonlinear reaction-diffusion equations in one space dimension with the
nonlinearity of bistable, ignition or monostable type. We prove a one-to-one
relation between the long time behavior of the solution and the limit value of
its energy for symmetric decreasing initial data in $L^2$ under minimal
assumptions on the nonlinearities. The obtained relation allows to establish
sharp threshold results between propagation and extinction for monotone
families of initial data in the considered general setting.

1
The categories of this paper are: cs
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex