Mathematical analysis for thin film capacitance via homogenization
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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 is
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.
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 is
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.
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