Identification of immersed obstacles via boundary measurements
@article{Alvarez2005IdentificationOI, title={Identification of immersed obstacles via boundary measurements}, author={Catalina Alvarez and Carlos Conca and Luis Friz and Otared Kavian and Jaime H. Ortega}, journal={Inverse Problems}, year={2005}, volume={21}, pages={1531 - 1552} }
We study the following inverse problem: an inaccessible rigid body D is immersed in a viscous fluid, in such a way that D plays the role of an obstacle around which the fluid is flowing in a greater bounded domain Ω, and we wish to determine D (i.e., its form and location) via boundary measurement on the boundary ∂Ω. Both for the stationary and the evolution problem, we show that under reasonable smoothness assumptions on Ω and D, one can identify D via the measurement of the velocity of the…
56 Citations
On the reconstruction of obstacles and of rigid bodies immersed in a viscous incompressible fluid
- Mathematics
- 2015
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…
Identification of obstacles immersed in a stationary Oseen fluid via boundary measurements
- MathematicsInverse Problems in Science and Engineering
- 2019
In this paper we consider the interior inverse problem of identifying a rigid boundary of an annular infinitely long cylinder within which there is a stationary Oseen viscous fluid, by measuring…
Size estimates of an obstacle in a stationary Stokes fluid
- Mathematics
- 2016
In this work we are interested in estimating the size of a cavity D immersed in a bounded domain Ω⊂Rd, d = 2, 3, filled with a viscous fluid governed by the Stokes system, by means of velocity and…
D ETECTING AN OBSTACLE IMMERSED IN A FLUID : THE S TOKES CASE
- Mathematics
- 2011
This paper presents a theoretical study of a detection of an object immersed in a fluid. The fluid motion is governed by the Stokes equations. We detail the Dirichlet case for which the results are…
Localization of small obstacles in Stokes flow
- Mathematics
- 2012
We want to detect small obstacles immersed in a fluid flowing in a larger bounded domain Ω in the three-dimensional case. We assume that the fluid motion is governed by the steady-state Stokes…
On the identification of a single body immersed in a Navier-Stokes fluid
- MathematicsEuropean Journal of Applied Mathematics
- 2007
In this work we consider the inverse problem of the identification of a single rigid body immersed in a fluid governed by the stationary Navier-Stokes equations. It is assumed that friction forces…
DETECTING AN OBSTACLE IMMERSED IN A FLUID BY SHAPE OPTIMIZATION METHODS
- Mathematics
- 2011
The paper presents a theoretical study of an identification problem by shape optimization methods. The question is to detect an object immersed in a fluid. Here, the problem is modeled by the Stokes…
Identification of a boundary obstacle in a Stokes fluid with Dirichlet--Navier boundary conditions: external measurements
- Mathematics
- 2022
The problem of identifying an obstruction into a fluid duct has several applications, one of them, for example in medicine the presence of Stenosis in coronary vessels is a life threatening disease.…
References
SHOWING 1-10 OF 17 REFERENCES
UNIQUE LOCALIZATION OF UNKNOWN BOUNDARIES IN A CONDUCTING MEDIUM FROM BOUNDARY MEASUREMENTS
- Mathematics
- 2002
We consider the problem of localizing an inaccessible piece I of the boundary of a conducting medium Ω, and a cavity D contained in Ω, from boundary measurements on the accessible part A of ∂Ω.…
Detecting an Inclusion in an Elastic Body by Boundary Measurements
- MathematicsSIAM Rev.
- 2002
It is proved that the volume (size) of D can be estimated, above and below, by an easily expressed quantity related to work depending only on the boundary traction and displacement.
Nonlinear Partial Differential Equations Using Compactness.
- Mathematics
- 1976
Abstract : After reviewing some general properties of Sobolev's spaces the author gives an abstract framework for Navier-Stokes equations. He examines some technical properties of the functional…
Stable determination of boundaries from Cauchy data
- Mathematics
- 1999
The problem of determining a portion $\Gamma$ of the boundary of a bounded planar domain $\Omega$ from Cauchy data arises in several contexts, for example, such as in corrosion detection from…
A uniqueness theorem for an inverse boundary value problem in electrical prospection
- Mathematics
- 1986
We show that a near constant conductivity of a two-dimensional body can be uniquely determined by steady state direct current measurements at the boundary. Mathematically, we show that the…
Detecting cavities by electrostatic boundary measurements
- Mathematics
- 2002
We prove upper and lower bounds on the size of an unknown cavity, or of a perfectly conducting inclusion, in an electrical conductor in terms of boundary measurements of voltage and current. Such…
A stability result in the localization of cavities in a thermic conducting medium
- Mathematics
- 2002
We prove a logarithmic stability estimate for a parabolic inverse problem concerning the localization of unknown cavities in a thermic conducting medium in n , n 2, from a single pair of boundary…
Determining Coefficients in a Class of Heat Equations via Boundary Measurements
- MathematicsSIAM J. Math. Anal.
- 2001
It is proved that knowledge of all possible pairs of input-output data determines uniquely the boundary spectral data of the underlying elliptic operator.
On an inverse boundary value problem
- Mathematics
- 2006
This paper is a reprint of the original work by A. P. Calderon published by the Brazilian Mathematical Society (SBM) in ATAS of SBM (Rio de Janeiro), pp. 65-73, 1980. The original paper had no…
Prolongement Unique Des Solutions
- Mathematics
- 1996
We prove a unique continuation property for solutions of Stokes equations with a non regular potential. For this, we state a Carleman's inequality which concerns the Laplace operator.