Stable determination of a vector field in a non-Self-Adjoint dynamical Schrödinger equation on Riemannian manifolds

Mourad Bellassoued; Ibtissem Ben Aïcha; Zouhour Rezig

doi:10.3934/mcrf.2020042

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2021, Volume 11, Issue 2: 403-431. Doi: 10.3934/mcrf.2020042

This issue Previous Article Local contact sub-Finslerian geometry for maximum norms in dimension 3 Next Article Extended backward stochastic Volterra integral equations and their applications to time-Inconsistent stochastic recursive control problems

Stable determination of a vector field in a non-Self-Adjoint dynamical Schrödinger equation on Riemannian manifolds

1.
Université Tunis El Manar, Ecole Nationale d'ingénieurs de Tunis, ENIT-LAMSIN, B.P. 37, 1002 Tunis, Tunisia
2.
Beijing Computational Science Research Center, Beijing 100193, China, and, Université Tunis El Manar, Faculté des Sciences de Tunis & ENIT-LAMSIN, B.P. 37, 1002 Tunis, Tunisia

^* Corresponding author: Mourad Bellassoued
^* Corresponding author: Mourad Bellassoued

Received: December 31, 2019

Revised: June 30, 2020

Early access: October 2020

Published: June 2021

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Abstract

This paper deals with an inverse problem for a non-self-adjoint Schrödinger equation on a compact Riemannian manifold. Our goal is to stably determine a real vector field from the dynamical Dirichlet-to-Neumann map. We establish in dimension $ n\geq2 $, an Hölder type stability estimate for the inverse problem under study. The proof is mainly based on the reduction to an equivalent problem for an electro-magnetic Schrödinger equation and the use of a Carleman estimate designed for elliptic operators.

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Mathematics Subject Classification: Primary: 35R30; Secondary: 58J32.

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