Recovering the twisting function in a twisted waveguide from the DN map

Mourad Choulli (1) , Eric Soccorsi (2)

1 LMAM - Laboratoire de Mathématiques et Applications de Metz
2 CPT - Centre de Physique Théorique - UMR 7332

We consider the inverse problem of determining the twisting function in a infinite cylindrical twisted waveguide from the corresponding DN map. This problem, which is naturally linked to some inverse anisotropic conductivity problem in a straight waveguide, remains generally open, unless 1) the twisting function is assumed to be affine, or, 2) its first derivative is sufficiently close to some a priori fixed constant. In both cases, we prove Lipschitz stability in the determination of the twisting function from a suitable DN map.

Mots clés: Dirichlet Laplacian; twisted infinite cylindrical waveguide; twisting function; DN map; stability estimate.; stability estimate

Domaines: Equations aux dérivées partielles [math.AP]

Mourad Choulli, Eric Soccorsi. Recovering the twisting function in a twisted waveguide from the DN map. 2012. ⟨hal-00735313v1⟩