No abstract

This work is concerned with a steady state Euler-Poisson system for potential flows arising in mathematical modeling for plasmas and semiconductors. We study the zero electron mass limit and zero relaxation time limit of the system by using the method of asymptotic expansions. These two limits are expressed by the Maxwell-Boltzmann relation and the classical drift-diffusion model, respectively. For each limit, we show the existence and uniqueness of profiles and justify the asymptotic expansions up to any order. These results also give new approaches for the convergence of the Euler-Poisson system to incompressible Euler equations, which has already been obtained via the quasineutral limit.

We give an example of supersonic solutions to a one-dimensional steady state Euler-Poisson system arising in the modeling of plasmas and semiconductors. The existence of the supersonic solutions which correspond to large current density is proved by Schauder's fixed point theorem. We show also the uniqueness of solutions in the supersonic region.