Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global existence and asymptotics for quasi-linear one-dimensional
  Klein-Gordon equations with mildly decaying Cauchy data   Let u be a solution to a quasi-linear Klein-Gordon equation in one-space
dimension, $\Box u + u = P (u, $\partial$\_t u, $\partial$\_x u; $\partial$\_t
$\partial$\_x u, $\partial$^2\_x u)$ , where P is a homogeneous polynomial of
degree three, and with smooth Cauchy data of size $\epsilon \rightarrow 0$. It
is known that, under a suitable condition on the nonlinearity, the solution is
global-in-time for compactly supported Cauchy data. We prove in this paper that
the result holds even when data are not compactly supported but just decaying
as $\langle x \rangle^ {--1}$ at infinity, combining the method of Klainerman
vector fields with a semiclassical normal forms method introduced by Delort.
Moreover, we get a one term asymptotic expansion for u when $t \rightarrow
+\infty$.

36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th