Stability of the determination of a coefficient for wave equations in an infinite waveguide

Yavar Kian (1, 2)

1 CPT - Centre de Physique Théorique - UMR 6207
2 CPT - Centre de Physique Théorique - UMR 7332

We consider the stability in the inverse problem consisting in the determination of an electric potential $q$, appearing in a Dirichlet initial-boundary value problem for the wave equation $\partial_t^2u-\Delta u+q(x)u=0$ in an unbounded wave guide $\Omega=\omega\times\R$ with $\omega$ a bounded smooth domain of $\R^2$, from boundary observations. The observation is given by the Dirichlet to Neumann map associated to a wave equation. We prove a Hölder stability estimate in the determination of $q$ from the Dirichlet to Neumann map. Moreover, provided that the gap between two electric potentials rich its maximum in a fixed bounded subset of $\overline{\Omega}$, we extend this result to the same inverse problem with measurements on a bounded subset of the lateral boundary $(0,T)\times\partial\Omega$.

Mots clés: problèmes inverses; équation des ondes; guide d'onde

Domaines: Equations aux dérivées partielles [math.AP]

Yavar Kian. Stability of the determination of a coefficient for wave equations in an infinite waveguide. Inverse Problems and Imaging , 2014, 8 (3), ⟨10.3934/ipi.2014.8.713⟩. ⟨hal-00824508⟩