Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variational Approach of Critical Sharp Front Speeds in Density-dependent
  Diffusion Model with Time Delay   For the classical reaction diffusion equation, the priori speed of fronts is
determined exactly in the pioneering paper (R.D. Benguria and M.C. Depassier,
{\em Commun. Math. Phys.} 175:221--227, 1996) by variational characterization
method. In this paper, we model the dispersal process using a density-dependent
diffusion equation with time delay. We show the existence and uniqueness of
sharp critical fronts, where the sharp critical front is $C^1$-smooth when the
diffusion degeneracy is weaker with $1<m<2$, and the sharp critical front is
non-$C^1$-smooth (piecewise smooth) when the diffusion degeneracy is stronger
with $m\ge 2$. We give a new variational approach for the critical wave speed
and investigate how the time delay affects the propagation mechanism of fronts.
Our results provide some interesting insight into the dynamics of critical
traveling wave.

15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ