Thin-film capacitance models

Abstract

Models for distributed capacitance in a thin film are derived in the form of a system of local RC diffusion equations coupled by a global elliptic equation. Such models contain the local geometry of the distributed capacitance on which charge pis stored and the exchange of current flux on its interface with the medium. Certain singular limits are characterized, and the resulting degenerate initial-boundary-value problems are shown to be well posed.

Keywords:

• Distributed RC circuits
• Microstructure
• Parabolic
• Pseudoparabolic

AMS:

• 35A05
• 35B27
• 35K50
• 35K90
• 35M20