# 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…

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## 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…

### 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.

### Determining conductivity by boundary measurements

- Mathematics
- 1984

A. P. Calderon pose la question: est-il possible de determiner la conductivite thermique d'un objet a partir de mesures statiques de la temperature et du flux de chaleur a la limite? On demontre que…