J. Korean Math. Soc. 2010; 47(6): 1223-1238
Printed November 1, 2010
https://doi.org/10.4134/JKMS.2010.47.6.1223
Copyright © The Korean Mathematical Society.
Soon-Yeong Chung
Sogang University
The purpose of this work is to identify the internal structure of the electrical networks with data obtained from only a part of network or the boundary of network. To be precise, it is discussed whether we can identify resistors or electrical conductivities of each link inside networks by the measurement of voltage on the boundary which is induced by a prescribed current on the boundary. As a result, it is shown that the structure of the resistor network can be determined uniquely by only one pair of the data (current, voltage) on the boundary, if the resistors satisfy an appropriate condition. Besides, several useful results about the energy functionals, which means the electrical power, are included.
Keywords: resistor network, Thompson's principle, inverse problem
MSC numbers: Primary 94C15; Secondary 94C05, 94C12
2007; 44(6): 1397-1415
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