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Characterization of the Gradient Blow-up of the Solution to the Conductivity Equation in the Presence of Adjacent Circular Inclusions by Lim, Mikyoung; Yu, Sanghyeon is a scholarly article available to read on EtoBox.

What is Characterization of the Gradient Blow-up of the Solution to the Conductivity Equation in the Presence of Adjacent Circular Inclusions about?

We consider the conductivity problem in the presence of adjacent circular inclusions having arbitrary constant conductivity. When two inclusions get closer and their conductivities degenerate to zero or infinity, the gradient of the solution can be arbitrary large. We characterize the gradient blow-up by deriving an explicit formula for the singular term of the solution in terms of the Lerch transcendent function. This derivation is valid for inclusions having arbitrary constant conductivity. We illustrate our results with numerical calculations.

Author

Lim, Mikyoung; Yu, Sanghyeon

Published

2013

Language

EN