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 (Tao Luo, Zhouping Xin, Commun. Math. Sci., 10:419–462, 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.

中文翻译：

---

非等熵 Euler-Poisson 系统跨音速激波解的非唯一性

在本文中，我们研究了非等熵 Euler-Poisson 系统，并获得了跨音速激波解的非唯一性。更准确地说，在有限长度的扁平喷嘴的边界上规定一类物理边界条件，我们证明存在两个且只有两个跨音速激波。这是由于等熵 Euler-Poisson 系统存在多个跨音速激波解的结果（Tao Luo, Zhouping Xin, Commun. Math. Sci ., 10:419–462, 2012）。此外，在跨音速激波的位置和喷嘴出口处的密度之间建立了具有阈值的单调性。