The Spherical Harmonics Expansion model coupled to the Poisson equation
Jan Haškovec, Nader Masmoudi, Christian Schmeiser, Mohamed Lazhar Tayeb · Kinetic and Related Models · 2011
The Spherical Harmonics Expansion (SHE) assumes a momentum distribution function only depending on themicroscopic kinetic energy. The SHE-Poisson systemdescribes carrier transport in semiconductors with self-induced electrostatic potential.Existence of weak solutions to the SHE-Poisson system subject to periodic boundary conditionsis established, based on appropriate a priori estimates and a Schauder fixed point procedure.The long time behavior of the one-dimensional Dirichlet problemwith well prepared boundary data is studied by an entropy-entropy dissipation method. Strong convergenceto equilibrium is proven. In contrast to earlier work, the analysis is carried out without the use of thederivation from a kinetic problem.