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Abstract
The regularized layered medium equotion is proposed as a model of voltage dist,ribution in a medium consisting of alternating thin films of conducting and dielectric riiaterials. This equation is obtained from the layered medium equation by the introdiiction of a regularizing perturbation that takes account of the resistance at the interface bet,ween adjacent conduct,ing and dielectric layers. The regularized equation is an inlplicit evolution equation which is shown to be well-posed. and an explicit measure is derived for the rate of decay of singularities in the initial data. It is shown that. as the regularizing parameter approaches zero, solutions of the initial-boiindary value problem for the regularized equation converge to the corresponding solution of the layered medium equation. This gives a method of calculating the exact rate of decay of singillarities in the initial data for the layered medium equation.