The Spherical Harmonics Expansion model coupled to the Poisson equation
Jan Haskovec - RICAM, Austrian Academy of Sciences, Altenbergerstrasse 69, Linz, A-4040, Austria (email)
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 SHE-Poisson 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.
Keywords: Spherical Harmonics Expansion model, Poisson equation, degenerate PDE, entropy, long time behavior.
Received: June 2011; Revised: October 2011; Published: November 2011.
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