Abstract
The electrochemical machining and electro-discharge machining of a metal objectto form a hole are considered. The processes are modelled as evolutionary elliptic free-boundary problems in which the electric potential satisfies Laplace's equation in the electrolyte and satisfies two conditions (one describing the rate of machining) on the surface of the object. The behaviour of the evolving boundary and some qualitative features of steady-state solutions are discussed.

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