Zero-electron-mass limit and zero-relaxation-time limit in a multi-dimensional stationary bipolar Euler–Poisson system

In this paper, we discuss a two- and three-dimensional stationary bipolar Euler–Poisson system from plasmas and semiconductor devices. We study the zero-electron-mass limit and the zero-relaxation-time limit of smooth subsonic solutions for the equations with proper boundary value conditions by using the method of matched asymptotic expansions. For each limit, we show the existence and uniqueness of profiles and justify the asymptotic expansions up to any order.