Diffusion limit of a semiconductor Boltzmann-Poisson system

Nader Masmoudi; Mohamed Lazhar Tayeb

doi:10.1137/050630763

Diffusion limit of a semiconductor Boltzmann-Poisson system

Nader Masmoudi, Mohamed Lazhar Tayeb

Research output: Contribution to journal › Article › peer-review

Abstract

The paper deals with the diffusion limit of the initial-boundary value problem for the multidimensional semiconductor Boltzmann-Poisson system. Here, we generalize the one-dimensional results obtained in [5] to the case of several dimensions using global renormalized solutions. The method of moments and a velocity averaging lemma are used to prove the convergence of the renormalized solutions to the semiconductor Boltzmann-Poisson system towards a global weak solution of the drift-diffusion-Poisson model.

Original language	English (US)
Pages (from-to)	1788-1807
Number of pages	20
Journal	SIAM Journal on Mathematical Analysis
Volume	38
Issue number	6
DOIs	https://doi.org/10.1137/050630763
State	Published - 2007

Keywords

Drift-diffusion model
Entropy dissipation
Kinetic transport equations
Moment method
Renormalized solution
Semiconductor Boltzmann-Poisson system
Velocity averaging lemma

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

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10.1137/050630763

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AB - The paper deals with the diffusion limit of the initial-boundary value problem for the multidimensional semiconductor Boltzmann-Poisson system. Here, we generalize the one-dimensional results obtained in [5] to the case of several dimensions using global renormalized solutions. The method of moments and a velocity averaging lemma are used to prove the convergence of the renormalized solutions to the semiconductor Boltzmann-Poisson system towards a global weak solution of the drift-diffusion-Poisson model.

KW - Drift-diffusion model

KW - Entropy dissipation

KW - Kinetic transport equations

KW - Moment method

KW - Renormalized solution

KW - Semiconductor Boltzmann-Poisson system

KW - Velocity averaging lemma

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Diffusion limit of a semiconductor Boltzmann-Poisson system

Abstract

Keywords

ASJC Scopus subject areas

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