STABILITY ESTIMATE FOR AN INVERSE PROBLEM FOR THE TIME HARMONIC MAGNETIC SCHRODINGERÖPERATOR FROM THE NEAR AND FAR FIELD PATTERNS

Mourad Bellassoued; Houssem Haddar; Amal Labidi

doi:10.1137/22m1481956

STABILITY ESTIMATE FOR AN INVERSE PROBLEM FOR THE TIME HARMONIC MAGNETIC SCHRODINGERÖPERATOR FROM THE NEAR AND FAR FIELD PATTERNS

Mourad Bellassoued
, Houssem Haddar
, Amal Labidi

University of Tunis El Manar

Research output: Contribution to journal › Article › peer-review

Abstract

We derive conditional stability estimates for inverse scattering problems related to the time harmonic magnetic Schrödinger equation. We prove logarithmic-type estimates for retrieving the magnetic (up to a gradient) and electric potentials from near field or far field maps. Our approach combines techniques from similar results obtained in the literature for inhomogeneous inverse scattering problems based on the use of geometrical optics solutions.

Original language	English
Pages (from-to)	2475-2504
Number of pages	30
Journal	SIAM Journal on Mathematical Analysis
Volume	55
Issue number	4
DOIs	https://doi.org/10.1137/22m1481956
Publication status	Published - 1 Jan 2023

Keywords

inverse medium scattering
inverse problems
magnetic potential
stability estimate

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10.1137/22m1481956

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title = "STABILITY ESTIMATE FOR AN INVERSE PROBLEM FOR THE TIME HARMONIC MAGNETIC SCHRODINGER{\"O}PERATOR FROM THE NEAR AND FAR FIELD PATTERNS",

abstract = "We derive conditional stability estimates for inverse scattering problems related to the time harmonic magnetic Schr{\"o}dinger equation. We prove logarithmic-type estimates for retrieving the magnetic (up to a gradient) and electric potentials from near field or far field maps. Our approach combines techniques from similar results obtained in the literature for inhomogeneous inverse scattering problems based on the use of geometrical optics solutions.",

keywords = "inverse medium scattering, inverse problems, magnetic potential, stability estimate",

author = "Mourad Bellassoued and Houssem Haddar and Amal Labidi",

note = "Publisher Copyright: {\textcopyright} 2023 Society for Industrial and Applied Mathematics.",

year = "2023",

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doi = "10.1137/22m1481956",

language = "English",

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AU - Bellassoued, Mourad

AU - Haddar, Houssem

AU - Labidi, Amal

PY - 2023/1/1

Y1 - 2023/1/1

N2 - We derive conditional stability estimates for inverse scattering problems related to the time harmonic magnetic Schrödinger equation. We prove logarithmic-type estimates for retrieving the magnetic (up to a gradient) and electric potentials from near field or far field maps. Our approach combines techniques from similar results obtained in the literature for inhomogeneous inverse scattering problems based on the use of geometrical optics solutions.

AB - We derive conditional stability estimates for inverse scattering problems related to the time harmonic magnetic Schrödinger equation. We prove logarithmic-type estimates for retrieving the magnetic (up to a gradient) and electric potentials from near field or far field maps. Our approach combines techniques from similar results obtained in the literature for inhomogeneous inverse scattering problems based on the use of geometrical optics solutions.

KW - inverse medium scattering

KW - inverse problems

KW - magnetic potential

KW - stability estimate

U2 - 10.1137/22m1481956

DO - 10.1137/22m1481956

M3 - Article

AN - SCOPUS:85166469375

SN - 0036-1410

VL - 55

SP - 2475

EP - 2504

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 4

ER -

STABILITY ESTIMATE FOR AN INVERSE PROBLEM FOR THE TIME HARMONIC MAGNETIC SCHRODINGERÖPERATOR FROM THE NEAR AND FAR FIELD PATTERNS

Abstract

Keywords

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