Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global Carleman estimates for waves and applications   In this article, we extensively develop Carleman estimates for the wave
equation and give some applications. We focus on the case of an observation of
the flux on a part of the boundary satisfying the Gamma conditions of Lions. We
will then consider two applications. The first one deals with the exact
controllability problem for the wave equation with potential. Following the
duality method proposed by Fursikov and Imanuvilov in the context of parabolic
equations, we propose a constructive method to derive controls that weakly
depend on the potentials. The second application concerns an inverse problem
for the waves that consists in recovering an unknown time-independent potential
from a single measurement of the flux. In that context, our approach does not
yield any new stability result, but proposes a constructive algorithm to
rebuild the potential. In both cases, the main idea is to introduce weighted
functionals that contain the Carleman weights and then to take advantage of the
freedom on the Carleman parameters to limit the influences of the potentials.

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The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph