Approximating the solutions to Euler-Poisson systems with boundary layers

Abstract

We aim to construct the approximate solutions to a Euler-Poisson system in an annular domain. A small parameter, multiplied to the highest order derivatives in the system, produces a singular behavior of the solutions. Among others, the sharp transitions near boundaries which are called boundary layers can occur. We explicitly construct the approximate solutions composed of the outer and inner expansions in the order of the small parameter. The equations for describing the boundary layers are determined from the inner expansions. In addition, here we effectively treat nonlinear terms using the Taylor polynomial expansions with multinomials. We also provide numerical evidence demonstrating the convergence of the approximate solutions to those of the Euler-Poisson system as the small parameter goes to zero