Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Slow dynamics for the hyperbolic Cahn-Hilliard equation in one space
  dimension   The aim of this paper is to study the metastable properties of the solutions
to a hyperbolic relaxation of the classic Cahn-Hilliard equation in one space
dimension, subject to either Neumann or Dirichlet boundary conditions. To
perform this goal, we make use of an "energy approach", already proposed for
various evolution PDEs, including the Allen-Cahn and the Cahn-Hilliard
equations. In particular, we shall prove that certain solutions maintain a {\it
$N$-transition layer structure} for a very long time, thus proving their
metastable dynamics. More precisely, we will show that, for an exponentially
long time, such solutions are very close to piecewise constant functions
assuming only the minimal points of the potential, with a finitely number of
transition points, which move with an exponentially small velocity.

13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex