Mejri Youssef - Inverse Problem: Stability for the aligned magnetic field by the Dirichlet-to-Neumann map for the wave equation in a periodic quantum waveguide

arima:1509 - Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, December 13, 2016, Volume 23 - 2016 - Special issue for LEM2I 2016 - https://doi.org/10.46298/arima.1509
Inverse Problem: Stability for the aligned magnetic field by the Dirichlet-to-Neumann map for the wave equation in a periodic quantum waveguide

Authors: Mejri Youssef

Dans ce papier, on a prouvé une estimation de stabilité pour le problème inverse de dé-termination du champ magnétique dans l'équation des ondes donné sur un domaine non borné à partir de l'opérateur de Dirichlet-to-Neumann. On a montré un résultat de stabilité pour ce problème inverse, dont la démonstration est basée sur la construction de solutions optique géométrique pour l'équation des ondes avec un potentiel magnétique 1-périodique. ABSTRACT. We consider the boundary inverse problem of determining the aligned magnetic field appearing in the magnetic wave equation in a periodic quantum cylindrical waveguide from boundary observations. The observation is given by the Dirichlet to Neumann map associated to the wave equation. We prove by means of the geometrical optics solutions of the magnetic wave equation that the knowledge of the Dirichlet-to-Neumann map determines uniquely the aligned magnetic field induced by a time independent and 1-periodic magnetic potential. We establish a Hölder-type stability estimate in the inverse problem.


Volume: Volume 23 - 2016 - Special issue for LEM2I 2016
Published on: December 13, 2016
Accepted on: December 12, 2016
Submitted on: December 9, 2016
Keywords: Magnetic wave equation,Dirichlet-to-Neumann map,Inverse problem,[MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]


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