Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reconstruction of the solution and the source of hyperbolic equations
  from boundary measurements: mixed formulations   We introduce a direct method allowing to solve numerically inverse type
problems for linear hyperbolic equations. We first consider the reconstruction
of the full solution of the wave equation posed in $\Omega\times (0,T)$ -
$\Omega$ a bounded subset of $\mathbb{R}^N$ - from a partial boundary
observation. We employ a least-squares technique and minimize the $L^2$-norm of
the distance from the observation to any solution. Taking the hyperbolic
equation as the main constraint of the problem, the optimality conditions are
reduced to a mixed formulation involving both the state to reconstruct and a
Lagrange multiplier. Under usual geometric optic conditions, we show the
well-posedness of this mixed formulation (in particular the inf-sup condition)
and then introduce a numerical approximation based on space-time finite
elements discretization. We prove the strong convergence of the approximation
and then discuss several examples for $N=1$ and $N=2$. The problem of the
reconstruction of both the state and the source term is also addressed.

13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat