A new formulation of the probe method and related problems

Abstract

The probe method gives a general idea to obtain a reconstruction formula of unknown objects embedded in a known background medium from a mathematical counterpart (the Dirichlet-to-Neumann map) of the measured data of some physical quantity on the boundary of the medium. It is based on the sequence of special solutions of the governing equation for the background medium related to a singular solution of the equation. In this paper the blowup property of the sequence is clarified. Moreover a new formulation of the probe method based on the property is given in some typical inverse boundary value problems.

arXiv comment4 figures, Final version. arXiv admin note: text overlap with arXiv:math/0611218

References in corpus (1)

• Reconstruction of inclusion from boundary measurements

Cited by in corpus (11)

• Monotonicity based shape reconstruction in electrical impedance tomography
• Superconductive and insulating inclusions for linear and non-linear conductivity equations
• Probe method and a Carleman function
• Revisiting the probe and enclosure methods
• Extracting discontinuity using the probe and enclosure methods
• The probe and enclosure methods for inverse obstacle scattering problems. The past and present
• Integrating the probe and singular sources methods :II. The Stokes system
• Integrating the probe and singular sources methods
• Travel Time and Heat Equation. One space dimensional case II
• Integrating the probe and singular sources methods: III. Mixed obstacle case
• Two sides of probe method and obstacle with impedance boundary condition