On an inverse problems for Laplace equations with potential terms on electrical networks
Commun. Korean Math. Soc. 2012 Vol. 27, No. 2, 243-255
https://doi.org/10.4134/CKMS.2012.27.2.243
Published online June 1, 2012
Ji Chan Chung, Du Hyeong Kim, and Tae Hoon Kwon
KAIST, Gyeonggi Science High School, Gyeonggi Science High School
Abstract : In this paper, we deal with an inverse problem for electrical resistor networks to detect the location of nodes where an extraordinary currents flow into or out of the nodes proportional to the potentials on them. To achieve the goal, we solve a special type of mixed boundary value problem for Laplace equations with potential terms on rectangular networks which plays a role as a forward problem. Then we solve an inverse problem to develop an algorithm to locate the node where the extraordinary current flows on it at most four times of measurements of potential and current on its boundary.
Keywords : trigonometric series, Hankel determinant, signal processing
MSC numbers : Primary 42A15; Secondary 15B05
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