DIFFUSION AND HOMOGENIZATION APPROXIMATION FOR SEMICONDUCTOR BOLTZMANN–POISSON SYSTEM

DOI10.1142/S0219891608001374zbMath1215.82052MaRDI QIDQ3520556

Mohamed Lazhar Tayeb, Nader Masmoudi

Publication date: 26 August 2008

Published in: Journal of Hyperbolic Differential Equations (Search for Journal in Brave)

zbMATH Keywords

diffusion approximationhomogenizationsemiconductorsrenormalized solutiontwo-scale convergencedrift-diffusion equationBoltzmann-Poisson systemaveraging lemma

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Statistical mechanics of semiconductors (82D37) Entropy in general topology (54C70) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics (82B21) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (8)

Homogenized diffusion limit of a Vlasov-Poisson-Fokker-Planck model ⋮ Homogenization and Hydrodynamic Limit for Fermi-Dirac Statistics Coupled to a Poisson Equation ⋮ On the Diffusion Limit of a Semiconductor Boltzmann–Poisson System Without Micro-Reversible Process ⋮ Homogenization of linear Boltzmann equations in the context of algebras with mean value ⋮ Diffusion regime with a high and oscillating field ⋮ Macroscopic approximation of a Fermi-Dirac statistics: Unbounded velocity space setting ⋮ Homogenization and diffusion approximation of the Vlasov–Poisson–Fokker–Planck system: A relative entropy approach ⋮ Homogenization of Boundary Layers in the Boltzmann--Poisson System

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