Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Alternating and variable controls for the wave equation   The present article discusses the exact observability of the wave equation
when the observation subset of the boundary is variable in time. In the
one-dimensional case, we prove an equivalent condition for the exact
observability, which takes into account only the location in time of the
observation. To this end we use Fourier series. Then we investigate the two
specific cases of single exchange of the control position, and of exchange at a
constant rate. In the multi-dimensional case, we analyse sufficient conditions
for the exact observability relying on the multiplier method. In the last
section, the multi-dimensional results are applied to specific settings and
some connections between the one and multi-dimensional case are discussed;
furthermore some open problems are presented.

16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg