Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Controllability of the semilinear wave equation governed by a
  multiplicative control   In this paper we establish several results on approximate controllability of
a semilinear wave equation by making use of a single multiplicative control.
These results are then applied to discuss the exact controllability properties
for the one dimensional version of the system at hand. The proof relies on
linear semigroup theory and the results on the additive controllability of the
semilinear wave equation. The approaches are constructive and provide explicit
steering controls. Moreover, in the context of undamped wave equation, the
exact controllability is established for a time which is uniform for all
initial states.

16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs