Sonic–supersonic–shock–subsonic–sonic solution to Euler–Poisson system with varying background charges

Abstract

In this paper, steady transonic shock solutions to the Euler–Poisson system are investigated with respect to varying background charge. More precisely, the density of the background charge is prescribed as a piecewise constant function whose discontinuity is determined only by the shock front. The Euler–Poisson system with varying background charge can describe the motion of the electrons in the special semiconductor devices. We establish the well-posedness of sonic–supersonic–shock–subsonic–sonic solutions, with sonic physical boundary conditions at the upstream and downstream respectively.