Inverse problems for linear hyperbolic equations using mixed formulations

We introduce in this document 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 distributed 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 discussed several examples for $N=1$ and $N=2$. The problem of the reconstruction of both the state and the source term is also addressed

International Outsourcing and Individual Job Separations

This paper studies the effects of international outsourcing on individual transitions out of jobs in the Danish manufacturing sector for the period 1992-2001. Estimation of a single risk duration model, where no distinction is made between different types of transitions out of the job, shows that outsourcing has a clear significant positive effect on the job separation rate, but the effect corresponds to a limited number of lost jobs. A competing risks duration model that distinguishes between job-to-job and job-to-unemployment transitions is also estimated. Outsourcing is found to increase the unemployment risk of workers and in particular low-skilled workers, but again the quantitative impact is not dramatic. Outsourcing also increases the job change hazard rate and mostly so for high-skilled workers.international outsourcing; job separations; competing risks duration model