Non-uniqueness Of Transonic Shock Solutions For Non-isentropic Euler-Poisson Equations

In this paper,we study the non-isentropic Euler-Poisson system and the non-uniqueness of transonic shock solutions is obtained.More precisely,prescribing a class of physical boundary conditions on the boundary of a flat nozzle with finite length,we prove that there exist two and only two transonic shocks.This is motivated by the result of existence of multiple transonic shock solutions for isentropic Euler-Poisson system,as clearly showed by Tao,Luo and Zhouping,Xin[Transonic shock solutions for a system of Euler-Poisson equations,Comm.Math.Sci.2012].Moreover,the monotonicity with a threshold between the location of the transonic shock and the density at the exit of the nozzle is established.