In this paper we consider the interior inverse problem of identifying a rigid boundary of an annular infinitely long cylinder within which there is a stationary Oseen viscous fluid, by measuring various quantities such as the fluid velocity, fluid traction (stress force) and/or the pressure gradient on portions of the outer accessible boundary of the annular geometry. The inverse problems are nonlinear with respect to the variable polar radius parameterizing the unknown star-shaped obstacle. Although for the type of boundary data that we are considering the obstacle can be uniquely identified based on the principle of analytic continuation, its reconstruction is still unstable with respect to small errors in the measured data. In order to deal with this instability, the nonlinear Tikhonov regularization is employed. Obstacles of various shapes are numerically reconstructed using the method of fundamental solutions for approximating the fluid velocity and pressure combined with the MATLAB toolbox routine lsqnonlin for minimizing the nonlinear Tikhonov's regularization functional subject to simple bounds on the variables.

中文翻译：

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通过边界测量识别浸入静止 Oseen 流体中的障碍物

在本文中，我们通过测量各种量，如流体速度、流体牵引力（应力）和/或环形几何形状的外部可接近边界部分上的压力梯度。对于参数化未知星形障碍物的可变极半径而言，逆问题是非线性的。虽然对于我们考虑的边界数据类型，障碍物可以根据解析延拓原理唯一识别，但对于测量数据中的小误差，其重建仍然不稳定。为了处理这种不稳定性，采用非线性 Tikhonov 正则化。