Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Energy decay rates for solutions of the wave equation with linear
  damping in exterior domain   In this paper we study the behavior of the energy of solutions of the wave
equation with localized damping in exterior domain. We assume that the damper
is positive at infinity. Under the Geometric Control Condition of Bardos et al
(1992), we prove that: 1) The total energy decay like O(1/t) and L^2-norm is
bounded for the solutions with initial data in (H_{0}^{1},L^{2}). 2) The total
energy and the square of the L^2-norm, repectively, decay like O(1/t^{2}) and
O(1/t) for a kind of the weighted initial data.

35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph