On an inverse problems for laplace equations with potential terms on electrical networks

Abstract

In this paper, we deal with an inverse problem for electrical resistor networks to detect the location of nodes where an extraordinary currents ow 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 ows on it at most four times of measurements of potential and current on its boundary. © 2012 The Korean Mathematical Society.