A. Jungel, ON THE EXISTENCE AND UNIQUENESS OF TRANSIENT SOLUTIONS OF A DEGENERATE NONLINEAR DRIFT-DIFFUSION MODEL FOR SEMICONDUCTORS, Mathematical models and methods in applied sciences, 4(5), 1994, pp. 677-703
We analyze the degenerate transient multi-dimensional quasi-hydrodynam
ic model for semiconductors with general recombination rate. We presen
t existence results for general nonlinear diffusivities for the nondeg
enerate and the degenerate Dirichlet-Neumann mixed boundary value prob
lem. Uniqueness of solutions of the nondegenerate system can be proved
in the Dirichlet boundary case. Concerning the degenerate problem uni
queness can only be shown under some conditions on the initial and bou
ndary data or on the electric field.