Khalifa Khelifi, Mohamed Abdelwahed, Nejmeddine Chorfi, Maatoug Hassine
Abstract:
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.
Submitted September 9, 2017. Published June 28, 2018.
Math Subject Classifications: 35J15, 78M22.
Key Words: Laplace operator; asymptotic analysis; topological gradient;
Kohn-Vogelius functional.
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Khalifa Khelifi Department of Mathematics College of Sciences Monastir University Monastir, Tunisia email: khalifakhelifi@hotmail.fr |
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Mohamed Abdelwahed Department of Mathematics College of Sciences King Saud University Riyadh, Saudi Arabia email: mabdelwahed@ksu.edu.sa |
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Nejmeddine Chorfi Department of Mathematics College of Sciences King Saud University Riyadh, Saudi Arabia email: nchorfi@ksu.edu.sa |
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Maatoug Hassine Department of Mathematics College of Sciences Monastir University Monastir, Tunisia email: Maatoug.Hassine@enit.rnu.tn |
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