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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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Volume 25, Issue 1

Issues

On the reconstruction of obstacles and of rigid bodies immersed in a viscous incompressible fluid

Jorge San Martín
  • Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, UMR 2071, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 170/3-Correo 3, Santiago, Chile
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/ Erica L. Schwindt
  • Departamento de Matemática, Facultad de Ciencias Exactas, Físico-Químicas y Naturales, Universidad Nacional de Río Cuarto, 5800 - Río Cuarto, Córdoba, Argentina
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/ Takéo Takahashi
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  • Inria, Villers-lès-Nancy, F-54600, France; and Université de Lorraine, IECL, UMR 7502, Vandoeuvre-lès-Nancy, F-54506, France; and CNRS, IECL, UMR 7502, Vandoeuvre-lès-Nancy, F-54506, France
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Published Online: 2015-12-09 | DOI: https://doi.org/10.1515/jiip-2014-0056

Abstract

We consider the geometrical inverse problem consisting in recovering an unknown obstacle in a viscous incompressible fluid by measurements of the Cauchy force on the exterior boundary. We deal with the case where the fluid equations are the nonstationary Stokes system and using the enclosure method, we can recover the convex hull of the obstacle and the distance from a point to the obstacle. With the same method, we can obtain the same result in the case of a linear fluid-structure system composed by a rigid body and a viscous incompressible fluid. We also tackle the corresponding nonlinear systems: the Navier–Stokes system and a fluid-structure system with free boundary. Using complex spherical waves, we obtain some partial information on the distance from a point to the obstacle.

Keywords: Geometrical inverse problems; fluid-structure interaction; Navier–Stokes system; enclosure method; complex geometrical solutions

MSC 2010: 35R30; 35Q35; 76D07; 35R35; 74F10; 76D05

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About the article

Received: 2014-08-04

Revised: 2015-09-25

Accepted: 2015-10-14

Published Online: 2015-12-09

Published in Print: 2017-02-01


Citation Information: Journal of Inverse and Ill-posed Problems, Volume 25, Issue 1, Pages 1–21, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2014-0056.

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