Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global existence and decay to equilibrium for some crystal surface
  models   In this paper we study the large time behavior of the solutions to the
following nonlinear fourth-order equations $$ \partial_t u=\Delta e^{-\Delta
u}, $$ $$ \partial_t u=-u^2\Delta^2(u^3). $$ These two PDE were proposed as
models of the evolution of crystal surfaces by J. Krug, H.T. Dobbs, and S.
Majaniemi (Z. Phys. B, 97, 281-291, 1995) and H. Al Hajj Shehadeh, R. V. Kohn,
and J. Weare (Phys. D, 240, 1771-1784, 2011), respectively. In particular, we
find explicitly computable conditions on the size of the initial data (measured
in terms of the norm in a critical space) guaranteeing the global existence and
exponential decay to equilibrium in the Wiener algebra and in Sobolev spaces.

30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph