February  2007, 1(1): 63-76. doi: 10.3934/ipi.2007.1.63

Reconstruction of obstacles immersed in an incompressible fluid

1. 

Technische Universität Darmstadt, Fachbereich Mathematik, Schlossgartenstr. 7, D-64289 Darmstadt, Germany

2. 

Department of Mathematics, University of Washington, Seattle, WA 98195-4350, United States

3. 

Department of Mathematics, Taida Institute of Mathematical Sciences, NCTS (Taipei), National Taiwan University, Taipei 106, Taiwan

Received  September 2006 Published  January 2007

We consider the reconstruction of obstacles inside a bounded domain filled with an incompressible fluid. Our method relies on special complex geometrical optics solutions for the stationary Stokes equation with a variable viscosity.
Citation: Horst Heck, Gunther Uhlmann, Jenn-Nan Wang. Reconstruction of obstacles immersed in an incompressible fluid. Inverse Problems and Imaging, 2007, 1 (1) : 63-76. doi: 10.3934/ipi.2007.1.63
[1]

Laurent Bourgeois, Jérémi Dardé. The "exterior approach" to solve the inverse obstacle problem for the Stokes system. Inverse Problems and Imaging, 2014, 8 (1) : 23-51. doi: 10.3934/ipi.2014.8.23

[2]

Marcin Bugdoł, Tadeusz Nadzieja. A nonlocal problem describing spherical system of stars. Discrete and Continuous Dynamical Systems - B, 2014, 19 (8) : 2417-2423. doi: 10.3934/dcdsb.2014.19.2417

[3]

Armin Lechleiter, Tobias Rienmüller. Factorization method for the inverse Stokes problem. Inverse Problems and Imaging, 2013, 7 (4) : 1271-1293. doi: 10.3934/ipi.2013.7.1271

[4]

A. Doubov, Enrique Fernández-Cara, Manuel González-Burgos, J. H. Ortega. A geometric inverse problem for the Boussinesq system. Discrete and Continuous Dynamical Systems - B, 2006, 6 (6) : 1213-1238. doi: 10.3934/dcdsb.2006.6.1213

[5]

Grégoire Allaire, Tuhin Ghosh, Muthusamy Vanninathan. Homogenization of stokes system using bloch waves. Networks and Heterogeneous Media, 2017, 12 (4) : 525-550. doi: 10.3934/nhm.2017022

[6]

Lekbir Afraites. A new coupled complex boundary method (CCBM) for an inverse obstacle problem. Discrete and Continuous Dynamical Systems - S, 2022, 15 (1) : 23-40. doi: 10.3934/dcdss.2021069

[7]

Rafał Kamocki, Marek Majewski. On the continuous dependence of solutions to a fractional Dirichlet problem. The case of saddle points. Discrete and Continuous Dynamical Systems - B, 2014, 19 (8) : 2557-2568. doi: 10.3934/dcdsb.2014.19.2557

[8]

Mohsen Tadi. A computational method for an inverse problem in a parabolic system. Discrete and Continuous Dynamical Systems - B, 2009, 12 (1) : 205-218. doi: 10.3934/dcdsb.2009.12.205

[9]

Abderrahmane Habbal, Moez Kallel, Marwa Ouni. Nash strategies for the inverse inclusion Cauchy-Stokes problem. Inverse Problems and Imaging, 2019, 13 (4) : 827-862. doi: 10.3934/ipi.2019038

[10]

Paolo Paoletti. Acceleration waves in complex materials. Discrete and Continuous Dynamical Systems - B, 2012, 17 (2) : 637-659. doi: 10.3934/dcdsb.2012.17.637

[11]

Gabriella Pinzari. Global Kolmogorov tori in the planetary $\boldsymbol N$-body problem. Announcement of result. Electronic Research Announcements, 2015, 22: 55-75. doi: 10.3934/era.2015.22.55

[12]

Bedr'Eddine Ainseba, Mostafa Bendahmane, Yuan He. Stability of conductivities in an inverse problem in the reaction-diffusion system in electrocardiology. Networks and Heterogeneous Media, 2015, 10 (2) : 369-385. doi: 10.3934/nhm.2015.10.369

[13]

Grégoire Allaire, Carlos Conca, Luis Friz, Jaime H. Ortega. On Bloch waves for the Stokes equations. Discrete and Continuous Dynamical Systems - B, 2007, 7 (1) : 1-28. doi: 10.3934/dcdsb.2007.7.1

[14]

Xu Zhang, Guanrong Chen. Boundedness of the complex Chen system. Discrete and Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021291

[15]

Gloria Paoli, Gianpaolo Piscitelli, Rossanno Sannipoli. A stability result for the Steklov Laplacian Eigenvalue Problem with a spherical obstacle. Communications on Pure and Applied Analysis, 2021, 20 (1) : 145-158. doi: 10.3934/cpaa.2020261

[16]

Mariano Giaquinta, Paolo Maria Mariano, Giuseppe Modica. A variational problem in the mechanics of complex materials. Discrete and Continuous Dynamical Systems, 2010, 28 (2) : 519-537. doi: 10.3934/dcds.2010.28.519

[17]

Jianfeng Feng, Mariya Shcherbina, Brunello Tirozzi. Dynamical behaviour of a large complex system. Communications on Pure and Applied Analysis, 2008, 7 (2) : 249-265. doi: 10.3934/cpaa.2008.7.249

[18]

Haibo Cui, Zhensheng Gao, Haiyan Yin, Peixing Zhang. Stationary waves to the two-fluid non-isentropic Navier-Stokes-Poisson system in a half line: Existence, stability and convergence rate. Discrete and Continuous Dynamical Systems, 2016, 36 (9) : 4839-4870. doi: 10.3934/dcds.2016009

[19]

Victor Isakov, Joseph Myers. On the inverse doping profile problem. Inverse Problems and Imaging, 2012, 6 (3) : 465-486. doi: 10.3934/ipi.2012.6.465

[20]

Shitao Liu, Roberto Triggiani. Determining damping and potential coefficients of an inverse problem for a system of two coupled hyperbolic equations. Part I: Global uniqueness. Conference Publications, 2011, 2011 (Special) : 1001-1014. doi: 10.3934/proc.2011.2011.1001

2020 Impact Factor: 1.639

Metrics

  • PDF downloads (162)
  • HTML views (0)
  • Cited by (15)

Other articles
by authors

[Back to Top]