Simultaneous determination of the magnetic field and the electric potential in the Schrödinger equation by a finite number of boundary observations-Reference-Cited by-同舟云学术

Simultaneous determination of the magnetic field and the electric potential in the Schrödinger equation by a finite number of boundary observations

Published:2018-04-01 Issue:2 Volume:26 Page:201-209
ISSN:1569-3945
Container-title:Journal of Inverse and Ill-posed Problems
language:
Short-container-title:

Author:

Ben Aïcha Ibtissem¹,Mejri Youssef²

Affiliation:

1. National Engineering School of Tunis, University of Tunis El Manar, ENIT-LAMSIN, B.P. 37, 1002Tunis, Tunisia

2. University of Aix-Marseille, 58 boulevard Charles Livon, 13284Marseille, France; and Faculty of Sciences of Bizerte, University of de Carthage, 7021 Jarzouna Bizerte, Tunisia

Abstract

AbstractWe study the inverse problem of determining the magnetic field and the electric potential appearing in the magnetic Schrödinger equation from the knowledge of a finite number of lateral observations of the solution. We prove a Lipschitz stability estimate for both coefficients simultaneously by choosing the “initial” conditions suitably.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/jiip-2017-0028/pdf

Reference26 articles.

1. Inverse problems for the Schrödinger equations with time-dependent electromagnetic potentials and the Aharonov–Bohm effect;J. Math. Phys.,2008

2. Uniqueness in the large of a class of multidimensional inverse problems;Dokl. Akad. Nauk SSSR,1981

3. Global identifiability for an inverse problem for the Schrödinger equation in a magnetic field;Math. Ann.,1995

4. A stability estimate for an inverse problem for the Schrödinger equation in a magnetic field from partial boundary measurements;Inverse Problems,2009

5. Determining damping and potential coefficients of an inverse problem for a system of two coupled hyperbolic equations. Part I: Global uniqueness;Discrete Contin. Dyn. Syst. Suppl.,2011

Cited by 7 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Partial Data Inverse Problems for the Nonlinear Time-Dependent Schrödinger Equation;SIAM Journal on Mathematical Analysis;2024-07-02

2. An inverse problem for data-driven prediction in quantum mechanics;J MATH PHYS;2024

3. Stability of a coefficient inverse problem for the discrete Schrödinger equation and a convergence result;Journal of Mathematical Analysis and Applications;2023-02

4. Uniqueness for time-dependent inverse problems with single dynamical data;Journal of Mathematical Analysis and Applications;2021-05

5. Stability estimates for time-dependent coefficients appearing in the magnetic Schrödinger equation from arbitrary boundary measurements;Inverse Problems & Imaging;2020