Identification of immersed obstacles via boundary measurements

Abstract

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 Q, and we wish to determine D (i.e., its form and location) via boundary measurement oil the boundary partial derivative Omega. Both for the stationary and the evolution problem, we show that under reasonable smoothness assumptions on Q 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 partial derivative Omega. 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.