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Stationary solutions to an energy model for semiconductor devices where the equations are defined on different domains
Author(s) -
Glitzky Annegret,
Hünlich Rolf
Publication year - 2008
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200710707
Subject(s) - uniqueness , mathematics , uniqueness theorem for poisson's equation , domain (mathematical analysis) , poisson's equation , function (biology) , dirichlet boundary condition , energy (signal processing) , boundary value problem , mathematical analysis , dirichlet distribution , poisson distribution , boundary (topology) , biology , statistics , evolutionary biology
We discuss a stationary energy model from semiconductor modelling. We accept the more realistic assumption that the continuity equations for electrons and holes have to be considered only in a subdomain Ω 0 of the domain of definition Ω of the energy balance equation and of the Poisson equation. Here Ω 0 corresponds to the region of semiconducting material, Ω \ Ω 0 represents passive layers. Metals serving as contacts are modelled by Dirichlet boundary conditions. We prove a local existence and uniqueness result for the two‐dimensional stationary energy model. For this purpose we derive a W 1, p ‐regularity result for solutions of systems of elliptic equations with different regions of definition and use the Implicit Function Theorem. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)