A Remark on the Enclosure Method for a Body with an Unknown Homogeneous Background Conductivity

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Abstract

Previous applications of the enclosure method with a finite set of observation data to a mathematical model of electrical impedance tomography are based on the assumption that the conductivity of the background body is homogeneous and known. This paper considers the case when the conductivity is homogeneous and unknown. It is shown that, in two dimensions if the domain occupied by the background body is enclosed by an ellipse, then it is still possible to extract some information about the location of unknown cavities or inclusions embedded in the body without knowing the background conductivity provided the Fourier series expansion of the voltage on the boundary does not contain high frequency parts (band limited) and satisfies a non vanishing condition of a quantity involving the Fourier coefficients.

Keywords

Enclosure method , inverse boundary value problem , cavity , inclusion , Laplace equation , exponentially growing solution
  • Masaru Ikehata Department of Mathematics, Graduate School of Engineering, Gunma University, Kiryu 376-8515, Japan.
  • Pages: 31–45
  • Date Published: 2008-07-01
  • Vol. 10 No. 2 (2008): CUBO, A Mathematical Journal

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Published

2008-07-01

How to Cite

[1]
M. Ikehata, “A Remark on the Enclosure Method for a Body with an Unknown Homogeneous Background Conductivity”, CUBO, vol. 10, no. 2, pp. 31–45, Jul. 2008.

Issue

Vol. 10 No. 2 (2008): CUBO, A Mathematical Journal

Section

Articles