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 , and we wish to determine D (i.e., its form and location) via boundary measurement on the boundary ∂. Both for the stationary and the evolution problem, we show that under reasonable smoothness assumptions on 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 ∂. 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.
Spectral and pseudospectral approximations of the heat equation are analyzed. The solution is represented in a suitable basis constructed with Hermite polynomials. Stability and convergence estimates are given and numerical tests are discussed.
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