Revisiting the probe and enclosure methods

DOI10.1088/1361-6420/ac70f2zbMath1491.35461arXiv2112.11645OpenAlexW4226006427MaRDI QIDQ5081805

Masaru Ikehata

Publication date: 17 June 2022

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.11645

zbMATH Keywords

enclosure methodinverse obstacle problemtime harmonic wave equationstationary Schrödinger equationimpenetrable obstacleprobe methodpenetrable obstacle

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Inverse problems for PDEs (35R30) Schrödinger operator, Schrödinger equation (35J10) Unilateral problems for linear elliptic equations and variational inequalities with linear elliptic operators (35J86)

Related Items (4)

A remark on the reconstruction formula of the support function for the magnetic Schrödinger operator ⋮ The enclosure method for semilinear elliptic equations with power-type nonlinearities ⋮ Comment on ‘Revisiting the probe and enclosure methods’ ⋮ Reply to Comment on ‘Revisiting the probe and enclosure methods’

Cites Work

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• A global uniqueness theorem for an inverse boundary value problem
• Reconstructing electromagnetic obstacles by the enclosure method
• Reconstructions from boundary measurements
• Uniqueness theorems for multidimensional inverse problems with unbounded coefficients
• Recovery of the shape of an obstacle and the boundary impedance from the far-field pattern
• Reconstruction of interfaces using CGO solutions for the Maxwell equations
• Two sides of probe method and obstacle with impedance boundary condition
• Reconstruction of the support function for inclusion from boundary measurements
• On the reconstruction of interfaces using complex geometrical optics solutions for the acoustic case
• The Enclosure Method for the Anisotropic Maxwell System
• Reconstruction of an obstacle from the scattering amplitude at a fixed frequency
• Reconstruction of the shape of the inclusion by boundary measurements
• Size estimation of inclusion
• How to draw a picture of an unknown inclusion from boundary measurements. Two mathematical inversion algorithms
• Reconstruction of inclusion from boundary measurements
• A new formulation of the probe method and related problems
• Enclosing a polygonal cavity in a two-dimensional bounded domain from Cauchy data
• Corrigendum: On the reconstruction of interfaces using complex geometrical optics solutions for the acoustic case
• Inverse Acoustic and Electromagnetic Scattering Theory
• Probe method and a Carleman function
• Reconstruction of obstacle from boundary measurements.

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