6533b7d8fe1ef96bd126b669
RESEARCH PRODUCT
Analysis of a Parabolic Cross-Diffusion Semiconductor Model with Electron-Hole Scattering
Li ChenAnsgar Jüngelsubject
Parabolic cylindrical coordinatesApplied MathematicsDegenerate energy levelsMathematical analysisBoundary value problemParabolic cylinder functionPoisson's equationGalerkin methodParabolic partial differential equationBackward Euler methodAnalysisMathematicsdescription
The global-in-time existence of non-negative solutions to a parabolic strongly coupled system with mixed Dirichlet–Neumann boundary conditions is shown. The system describes the time evolution of the electron and hole densities in a semiconductor when electron-hole scattering is taken into account. The parabolic equations are coupled to the Poisson equation for the electrostatic potential. Written in the quasi-Fermi potential variables, the diffusion matrix of the parabolic system contains strong cross-diffusion terms and is only positive semi-definite such that the problem is formally of degenerate type. The existence proof is based on the study of a fully discretized version of the system, using a backward Euler scheme and a Galerkin method, on estimates for the free energy, and careful weak compactness arguments.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2007-01-04 | Communications in Partial Differential Equations |