Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diffusive stability against nonlocalized perturbations of planar wave
  trains in reaction-diffusion systems   Planar wave trains are traveling wave solutions whose wave profiles are
periodic in one spatial direction and constant in the transverse direction. In
this paper, we investigate the stability of planar wave trains in
reaction-diffusion systems. We establish nonlinear diffusive stability against
perturbations that are bounded along a line in $\mathbb{R}^2$ and decay
exponentially in the distance from this line. Our analysis is the first to
treat spatially nonlocalized perturbations that do not originate from a phase
modulation. We also consider perturbations that are fully localized and
establish nonlinear stability with better decay rates, suggesting a trade-off
between spatial localization of perturbations and temporal decay rate. Our
stability analysis utilizes pointwise estimates to exploit the spatial
structure of the perturbations. The nonlocalization of perturbations prevents
the use of damping estimates in the nonlinear iteration scheme; instead, we
track the perturbed solution in two different coordinate systems.

24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an