[Back]

A. Jüngel, L. Chen:
"Analysis of a Parabolic Cross-Diffusion Semiconductor Model with Electron-Hole Scattering";
Communications in Partial Differential Equations, 32 (2007), 127 - 148.

The global-in-time existence of nonnegative 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.

Siehe englischen Abstract.

Cross-diffusion system, degenerate parabolic equations, free energy, existence of weak solutions