Non-uniqueness of transonic shock solutions to non-isentropic Euler-Poisson system with varying background charges

Transonic shock solutions to non-isentropic Euler-Poisson system with varying background charges in a one-dimensional nozzle are studied in this paper. More precisely, the value of the background charge is associated with the transonic shock solutions and varies with the shock location. For given appropriate physical conditions, we derive the monotonicity of the density at the exit of the nozzle with respect to the shock location. Furthermore, the existence and non-uniqueness of transonic shocks are obtained.