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<p>This paper addresses the problem of detecting an obstacle immersed in a Stokes flow from boundary measurements. The inverse problem is formulated within the framework of shape optimization, as the minimization of a least-squares misfit functional. We first establish a shape identifiability result for non-axisymmetric fluid-obstacle configurations and a perfect slip condition on the obstacle boundary and we discuss the axisymmetric case. Next, under suitable smoothness assumptions, first and second order shape derivatives of the cost functional are computed. As a consequence, by showing that the Riesz operator associated with the shape Hessian is compact, we conclude to the instability of the considered inverse problem.</p>

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Second order shape sensitivity analysis for an inverse obstacle problem with Navier boundary conditions

  • 期刊论文

  • 发表日期：

    2026年6月27日

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  • Chaima Bsaies,
  • Raja Dziri

摘要

This paper addresses the problem of detecting an obstacle immersed in a Stokes flow from boundary measurements. The inverse problem is formulated within the framework of shape optimization, as the minimization of a least-squares misfit functional. We first establish a shape identifiability result for non-axisymmetric fluid-obstacle configurations and a perfect slip condition on the obstacle boundary and we discuss the axisymmetric case. Next, under suitable smoothness assumptions, first and second order shape derivatives of the cost functional are computed. As a consequence, by showing that the Riesz operator associated with the shape Hessian is compact, we conclude to the instability of the considered inverse problem.