QUALITATIVE BEHAVIOR OF SOLUTIONS OF A DEGENERATE NONLINEAR DRIFT-DIFFUSION MODEL FOR SEMICONDUCTORS

We are concerned with qualitative properties of transient solutions of a degenerate multidimensional quasi-hydrodynamic model for semiconductors with nonlinear diffusivities. For small time and sufficiently small initial and boundary data we show a local vanishing property of a solution. Furthermore it is shown that the carrier densities are bounded uniformly in time and are strictly positive uniformly in time if the recombination-generation rate satisfies some structural assumption. Finally we construct a Lyapunov functional in order to show convergence of the carrier distributions to the thermal equilibrium state as the time tends to infinity.