Some asymptotic analysis in steady‐state Euler–Poisson equations for potential flow

Abstract

We study the zero‐electron‐mass limit, the zero‐relaxation‐time limit and the quasi‐neutral limit in steady‐state Euler–Poisson system for potential flow arising in mathematical modeling for plasmas and semiconductors. We show the existence and uniqueness of solutions when the electron‐mass is small enough. For the zero‐electron‐mass limit and the zero‐relaxation‐time limit, we prove the strong convergence of the sequence of solutions and give the corresponding error estimates. Whereas for the quasi‐neutral limit, we obtain the similar results only if the given data on the boundary are in equilibrium.