Asymptotic formula for detecting inclusions via boundary measurements

Asymptotic formula for detecting inclusions via boundary measurements

In this article, we are concerned with a geometric inverse problem related to the Laplace operator in a three-dimensional domain. The aim is to derive an asymptotic formula for detecting an inclusion via boundary measurement. The topological sensitivity method is applied to calculate a high-orde...

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Main Authors: Khalifa Khelifi, Mohamed Abdelwahed, Nejmeddine Chorfi, Maatoug Hassine
Format: Article
Language:English
Published: Texas State University 2018-06-01
Series:Electronic Journal of Differential Equations
Subjects:
Laplace operator
asymptotic analysis
topological gradient
Kohn-Vogelius functional
Online Access:http://ejde.math.txstate.edu/Volumes/2018/134/abstr.html
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spelling doaj-a64df5c2320f4700aff40d5a1ab25c7f2020-11-24T22:30:47ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912018-06-012018134,116Asymptotic formula for detecting inclusions via boundary measurementsKhalifa Khelifi0Mohamed Abdelwahed1Nejmeddine Chorfi2Maatoug Hassine3 Monastir Univ., Monastir, Tunisia King Saud Univ., Riyadh, Saudi Arabia King Saud Univ., Riyadh, Saudi Arabia Monastir Univ., Monastir, Tunisia In this article, we are concerned with a geometric inverse problem related to the Laplace operator in a three-dimensional domain. The aim is to derive an asymptotic formula for detecting an inclusion via boundary measurement. The topological sensitivity method is applied to calculate a high-order topological asymptotic expansion of the semi-norm Kohn-Vogelius functional, when a Dirichlet perturbation is introduced in the initial domain.http://ejde.math.txstate.edu/Volumes/2018/134/abstr.htmlLaplace operatorasymptotic analysistopological gradientKohn-Vogelius functional
collection DOAJ
language English
format Article
sources DOAJ
author Khalifa Khelifi
Mohamed Abdelwahed
Nejmeddine Chorfi
Maatoug Hassine
spellingShingle Khalifa Khelifi
Mohamed Abdelwahed
Nejmeddine Chorfi
Maatoug Hassine
Asymptotic formula for detecting inclusions via boundary measurements
Electronic Journal of Differential Equations
Laplace operator
asymptotic analysis
topological gradient
Kohn-Vogelius functional
author_facet Khalifa Khelifi
Mohamed Abdelwahed
Nejmeddine Chorfi
Maatoug Hassine
author_sort Khalifa Khelifi
title Asymptotic formula for detecting inclusions via boundary measurements
title_short Asymptotic formula for detecting inclusions via boundary measurements
title_full Asymptotic formula for detecting inclusions via boundary measurements
title_fullStr Asymptotic formula for detecting inclusions via boundary measurements
title_full_unstemmed Asymptotic formula for detecting inclusions via boundary measurements
title_sort asymptotic formula for detecting inclusions via boundary measurements
publisher Texas State University
series Electronic Journal of Differential Equations
issn 1072-6691
publishDate 2018-06-01
description In this article, we are concerned with a geometric inverse problem related to the Laplace operator in a three-dimensional domain. The aim is to derive an asymptotic formula for detecting an inclusion via boundary measurement. The topological sensitivity method is applied to calculate a high-order topological asymptotic expansion of the semi-norm Kohn-Vogelius functional, when a Dirichlet perturbation is introduced in the initial domain.
topic Laplace operator
asymptotic analysis
topological gradient
Kohn-Vogelius functional
url http://ejde.math.txstate.edu/Volumes/2018/134/abstr.html
work_keys_str_mv AT khalifakhelifi asymptoticformulafordetectinginclusionsviaboundarymeasurements
AT mohamedabdelwahed asymptoticformulafordetectinginclusionsviaboundarymeasurements
AT nejmeddinechorfi asymptoticformulafordetectinginclusionsviaboundarymeasurements
AT maatoughassine asymptoticformulafordetectinginclusionsviaboundarymeasurements
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