Inverse Crack Problem and Probe Method

  • 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.

Published
2006-04-01
How to Cite
Ikehata, M. (2006). Inverse Crack Problem and Probe Method. CUBO, A Mathematical Journal, 8(1), 29–40. Retrieved from http://revistas.ufro.cl/ojs/index.php/cubo/article/view/1610