An inverse stability result for non-compactly supported potentials by one arbitrary lateral Neumann observation

M Bellassoued (1, 2) , Y Kian (3, 4) , Eric Soccorsi (3, 4)

1 FDP - Fédération de recherche Denis Poisson
2 UCAR - Université de Carthage (Tunisie)
3 CPT - Centre de Physique Théorique - UMR 7332
4 CPT - E8 Dynamique quantique et analyse spectrale

In this paper we investigate the inverse problem of determining the time independent scalar potential of the dynamic Schrödinger equation in an infinite cylindrical domain, from partial measurement of the solution on the boundary. Namely, if the potential is known in a neighborhood of the boundary of the spatial domain, we prove that it can be logarithmic stably determined in the whole waveguide from a single observation of the solution on any arbitrary strip-shaped subset of the boundary.

Mots clés: Inverse Problems; Schrödinger equation; Infinite cylindrical waveguide; Carleman estimate; Stability estimate.

Domaines: Equations aux dérivées partielles [math.AP]

M Bellassoued, Y Kian, Eric Soccorsi. An inverse stability result for non-compactly supported potentials by one arbitrary lateral Neumann observation. Journal of Differential Equations, 2016, 260 (10), pp.7535-7562. ⟨10.1016/j.jde.2016.01.033⟩. ⟨hal-01180254⟩