Inverse Crack Problem and Probe Method

Masaru Ikehata

Authors

Masaru Ikehata Department oí Mathematics, Faculty of Engineering Gunma University, Kiryu 376-8515, Japan.

Keywords:

inverse boundary value problem, probe method, crack, Dirichlet-to-Neumann map, Laplace equation, indicator function, needle, nondestructive evaluation

Abstract

A problem of extracting information about the location and shape of unknown cracks in a background medium from the Dirichlet-to-Neumann map is considered. An application of a new formulation of the probe method introduced by the author to the problem is given. The method is based on: the blowup property of sequences of special solutions of the governing equation for the background medium which are related to a singular solution of the equation; an explicit lower bound of an L²-norm of the gradient of the so-called reflected solution.