6533b851fe1ef96bd12aa025
RESEARCH PRODUCT
ANALYSIS OF A SPHERICAL HARMONICS EXPANSION MODEL OF PLASMA PHYSICS
Ansgar JüngelOlaf Hansensubject
Applied MathematicsMathematical analysisZonal spherical harmonicsBoundary (topology)Spherical harmonicssymbols.namesakeModeling and SimulationDirichlet boundary conditionSpin-weighted spherical harmonicssymbolsVector spherical harmonicsUniquenessMathematicsSolid harmonicsdescription
A spherical harmonics expansion model arising in plasma and semiconductor physics is analyzed. The model describes the distribution of particles in the position-energy space subject to a (given) electric potential and consists of a parabolic degenerate equation. The existence and uniqueness of global-in-time solutions is shown by semigroup theory if the particles are moving in a one-dimensional interval with Dirichlet boundary conditions. The degeneracy allows to show that there is no transport of particles across the boundary corresponding to zero energy. Furthermore, under certain conditions on the potential, it is proved that the solution converges in the long-time limit exponentially fast to some steady state.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2004-05-01 | Mathematical Models and Methods in Applied Sciences |