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Integral equations for an inverse boundary value problem for the two-dimensional Stokes equations. (English) Zbl 1136.35101
In this paper the author investigates the inverse problem of determining the shape and location of a rigid body immersed in a fluid, on the base of prescribed data and measured quantities, namely, the traction at the boundary of the system “fluid-solid”. The paper extends the reciprocity gap principle to the problem to recover the location and shape from the measured velocity and traction at the exterior boundary of the fluid, that is to an inverse boundary value problem for the Stokes equation.
The author derives the systems of integral equations equivalent to the inverse problem. Then the integral equations are rewritten in terms of the parameterizations of the curves occurring in the equations. The mathematical foundation of this extension is provided. An iteration scheme that uses a Tikhonov regularization is derived. Some numerical examples illustrate the method.

35R30 Inverse problems for PDEs
35Q30 Navier-Stokes equations
45Q05 Inverse problems for integral equations
65R32 Numerical methods for inverse problems for integral equations
Full Text: DOI
[1] DOI: 10.1088/0266-5611/21/5/003 · Zbl 1088.35080
[2] DOI: 10.1016/j.matcom.2004.02.007 · Zbl 1075.76020
[3] Eng. Analysis Bound. Elem. 28 pp 1245– (2005)
[4] DOI: 10.1016/0093-6413(93)90032-J · Zbl 0801.73021
[5] Chang I-D., Arch. Rat. Mech. An. 7 pp 389– (1961)
[6] DOI: 10.1216/jiea/1181075363 · Zbl 1139.45003
[7] DOI: 10.1002/(SICI)1099-1476(20000125)23:2<103::AID-MMA106>3.0.CO;2-4 · Zbl 0951.35133
[8] Kress R., Inverse Problems 21 pp 4– (2005) · Zbl 1071.35123
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