Homogenization of Boundary Layers in the Boltzmann--Poisson System

DOI10.1137/18M1193888zbMath1467.82039OpenAlexW3136480851MaRDI QIDQ5857933

Clemens Heitzinger, José A. Morales E.

Publication date: 8 April 2021

Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/18m1193888

zbMATH Keywords

homogenizationnanowire sensorsBoltzmann-Poisson system

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Classical dynamic and nonequilibrium statistical mechanics (general) (82C05) Homogenization in optics and electromagnetic theory (78M40) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Boltzmann equations (35Q20)

Cites Work

• A transport equation for confined structures derived from the Boltzmann equation
• Existence and local uniqueness for 3D self-consistent multiscale models of field-effect sensors
• Diffusion approximation for the one-dimensional Boltzmann-Poisson system
• Multiscale Modeling of Planar and Nanowire Field-Effect Biosensors
• A pedagogical approach to the Magnus expansion
• DIFFUSION AND HOMOGENIZATION APPROXIMATION FOR SEMICONDUCTOR BOLTZMANN–POISSON SYSTEM
• Multiscale Methods
• Diffusion Approximation and Homogenization of the Semiconductor Boltzmann Equation

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