重构双调和方程中的未知内含物

Reconstructing a potential perturbation of the biharmonic operator on transversally anisotropic manifolds

We prove that a continuous potential $q$ can be constructively determined from the knowledge of the Dirichlet-to-Neumann map for the perturbed biharmonic operator $Δ_g^2+q$ on a conformally transversally anisotropic Riemannian manifold of dimension $\ge 3$ with boundary, assuming that the geodesic ray transform on the transversal manifold is constructively invertible. This is a constructive counterpart of the uniqueness result of [51]. In particular, our result is applicable and new in the case of smooth bounded domains in the $3$-dimensional Euclidean space as well as in the case of $3$-dimen…

双调和波逆腔体散射问题的采样方法

Sampling methods for the inverse cavity scattering problem of biharmonic waves

针对弹性薄板中固支腔体的反演问题，本文强化了双调和波远场测量下的线性采样方法分析，并实现有限孔径下的线性与扩展采样方法，数值实验验证了二者的有效性与鲁棒性。

吸收性可穿透散射体双调和散射问题的因子分解方法

Factorization method for the biharmonic scattering problem for an absorbing penetrable scatterer

本文将因子分解方法拓展至薄弹性板中吸收性可穿透散射体的逆散射问题，基于双调和波动方程严格证明该方法的合理性，提供二元判据区分采样点位置，并数值分析弱散射体Born近似的有效性。

双曲波逆散射问题的直接成像方法：带相位和无相位数据

A direct imaging method for inverse scattering problem of biharmonic wave with phased and phaseless data

本文提出基于反时间迁移的直接成像方法，用于恢复具有四种边界条件之一的扩展障碍物，利用单一测量数据类型进行障碍物形状和位置的识别。

A direct method for reconstructing inclusions and boundary conditions from electrostatic data

In this paper, we will discuss the use of a Sampling Method to reconstruct impenetrable inclusions from Electrostatic Cauchy data. We consider the case of a perfectly conducting and impedance inclusion. In either case, we show that the Dirichlet to Neumann mapping can be used to reconstruct impenetrable sub-regions via a sampling method. We also propose a non-iterative method based on boundary integral equations to reconstruct the impedance parameter using the reconstructed boundary of the inclusion from the knowledge of multiple Cauchy pairs which can be computed from Dirichlet to Neumann map…

Localized sensitivity analysis at high-curvature boundary points of reconstructing inclusions in transmission problems

In this paper, we are concerned with the recovery of the geometric shapes of inhomogeneous inclusions from the associated far field data in electrostatics and acoustic scattering. We present a local resolution analysis and show that the local shape around a boundary point with a high magnitude of mean curvature can be reconstructed more easily and stably. In proving this, we develop a novel mathematical scheme by analyzing the generalized polarisation tensors (GPTs) and the scattering coefficients (SCs) coming from the associated scattered fields, which in turn boils down to the analysis of th…