• DOI:10.1088/0266-5611/21/5/003
• Corpus ID: 122521854

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}
}

• C. Alvarez, C. Conca, +2 authors Jaime H. Ortega
• Published 1 October 2005
• Mathematics
• Inverse Problems

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 fluid and the Cauchy forces on some part of the boundary ∂Ω. We also show that the dependence of the Cauchy forces on deformations of D is analytic, and give some stability results for the inverse problem.