Electron. J. Differential Equations, Vol. 2017 (2017), No. 233, pp. 1-9.

Determination of obstacles in Stokes flow by boundary measurement

Mohamed Abdelwahed, Montassar Barhoumi, Nejmeddine Chorfi

Abstract:
We study the determination of some obstacles in a Stokes flow domain with overdetermined boundary data. We use a method based on the topological sensitivity technique associated to the reciprocity gap function concept. We develop an asymptotic formula between the flow parameters and the boundary data. The obtained formula is interesting and serve as a useful tool to develop an accurate and robust numerical method in geometry inverse problems.

Submitted July 29, 2017. Published September 25, 2017.
Math Subject Classifications: 35N25, 49K40.
Key Words: Stokes flow; reciprocity gap function; calculus of variations; topological sensitivity.

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Mohamed Abdelwahed
Department of Mathematics, College of Sciences
King Saud University
Riyadh, Saudi Arabia
email: mabdelwahed@ksu.edu.sa
Montassar Barhoumi
Department of Mathematics
ESSTHS, Sousse University
Sousse University, Tunisia
email: montassar.barhoumi2014@gmail.com
Nejmeddine Chorfi
Department of Mathematics, College of Sciences
King Saud University
Riyadh, Saudi Arabia
email: nchorfi@ksu.edu.sa

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