Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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THE FAULTY RESISTOR PROBLEMS AND THE INVERSE SOURCE PROBLEMS FOR RECTANGULAR ELECTRICAL NETWORKS

  • Published : 2009.07.31
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Abstract

This paper ultimately aims to develop noninvasive techniques to identify the inside of a given electrical network. Based on the theory of the partial differentiation equations and mathematical modeling, this paper devises the algorithms to find the locations of possible abnormalities. To ensure the certainty of the algorithms, this study restricted the forms of the network and the number of abnormalities, rendering it easy to prove the uniqueness of the position of the abnormalities.

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References

  1. S.-Y. Chung and C. A. Berenstein, $\omega$-harmonic functions and inverse conductivity problems on networks, SIAM J. Appl. Math. 65 (2002), no. 4, 1039–1046
  2. E. Curtis and J. Morrow, The Dirichlet to Neumann map for a resistor network, SIAM J. Appl. Math. 51 (1991), no. 4, 1011–1029 https://doi.org/10.1137/0151051
  3. E. Curtis and J. Morrow, Inverse Problems for Electrical Networks, World Scientific, 2000

Cited by

  1. ON AN INVERSE PROBLEMS FOR LAPLACE EQUATIONS WITH POTENTIAL TERMS ON ELECTRICAL NETWORKS vol.27, pp.2, 2012, https://doi.org/10.4134/CKMS.2012.27.2.243