From Bipolar Euler-Poisson System to Unipolar Euler-Poisson One in the Perspective of Mass

The main purpose of this paper is to provide an effective procedure to study rigorously the relationship between unipolar and bipolar Euler-Poisson systems in the perspective of mass. Based on the fact that the mass of an electron is far less than that of an ion, we amplify this property by letting me/mi→0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_e/m_i\rightarrow 0$$\end{document} and using two different singular limits to illustrate it, which are the zero-electron mass limit and the infinity-ion mass limit. We use the method of asymptotic expansions to handle the problem and find that the limiting process from bipolar to unipolar systems is actually the process of decoupling, but not the vanishing of equations of the corresponding the other particle.