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 2011

Fingerprint

Coupled Model
Spherical Harmonics
Poisson equation
Poisson's equation
Entropy
Entropy Dissipation
Convergence to Equilibrium
Carrier transport
Existence of Weak Solutions
Long-time Behavior
A Priori Estimates
Periodic Boundary Conditions
Kinetic energy
Strong Convergence
Electrostatics
Dirichlet Problem
Distribution functions
Semiconductors
Momentum
Siméon Denis Poisson

Keywords

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

ASJC Scopus subject areas

  • Modeling and Simulation
  • Numerical Analysis

Cite this

The spherical harmonics expansion model coupled to the poisson equation. / Haskovec, Jan; Masmoudi, Nader; Schmeiser, Christian; Tayeb, Mohamed Lazhar.

In: Kinetic and Related Models, Vol. 4, No. 4, 12.2011, p. 1063-1079.

Research output: Contribution to journalArticle

Haskovec, Jan ; Masmoudi, Nader ; Schmeiser, Christian ; Tayeb, Mohamed Lazhar. / The spherical harmonics expansion model coupled to the poisson equation. In: Kinetic and Related Models. 2011 ; Vol. 4, No. 4. pp. 1063-1079.
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