Inverse Crack Problem and Probe Method

Downloads

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.

Keywords

inverse boundary value problem , probe method , crack , Dirichlet-to-Neumann map , Laplace equation , indicator function , needle , nondestructive evaluation
  • Masaru Ikehata Department oí Mathematics, Faculty of Engineering Gunma University, Kiryu 376-8515, Japan.
  • Pages: 29–40
  • Date Published: 2006-04-01
  • Vol. 8 No. 1 (2006): CUBO, A Mathematical Journal

Downloads

Download data is not yet available.

Published

2006-04-01

How to Cite

[1]
M. Ikehata, “Inverse Crack Problem and Probe Method”, CUBO, vol. 8, no. 1, pp. 29–40, Apr. 2006.

Issue

Vol. 8 No. 1 (2006): CUBO, A Mathematical Journal

Section

Articles