The Regularized Layered Medium Equation
نویسندگان
چکیده
The regularized layered medium equation is proposed as a model of voltage distribution in a medium consisting of alternating thin films of conducting and dielectric materials. This equation is obtained from the layered medium equation by the introduction of a regularizing perturbation that takes account of the resistance at the interface between adjacent conducting and dielectric layers. The regularized equation is an implicit 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-boundary 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 singularities in the initial data for the layered medium equation. AMS Subject Classification: 35A05, 35K22, 35K55, 47H05, 47H06, 47H15
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