The spherical harmonics expansion model coupled to the poisson equation

Jan Haskovec, Nader Masmoudi, Christian Schmeiser, Mohamed Lazhar Tayeb

Research output: Contribution to journalArticle

Abstract

The Spherical Harmonics Expansion (SHE) assumes a momentum distribution function only depending on the microscopic kinetic energy. The SHE-Poisson system describes carrier transport in semiconductors with self-induced electrostatic potential. Existence of weak solutions to the SHEPoisson system subject to periodic boundary conditions is established, based on appropriate a priori estimates and a Schauder fixed point procedure. The long time behavior of the one-dimensional Dirichlet problem with well prepared boundary data is studied by an entropy-entropy dissipation method. Strong convergence to equilibrium is proven. In contrast to earlier work, the analysis is carried out without the use of the derivation from a kinetic problem.

Original languageEnglish (US)
Pages (from-to)1063-1079
Number of pages17
JournalKinetic and Related Models
Volume4
Issue number4
DOIs
StatePublished - Dec 1 2011

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Keywords

  • Degenerate PDE
  • Entropy
  • Long time behavior
  • Poisson equation
  • Spherical harmonics expansion model

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation

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