Communications in Mathematical Sciences

Volume 19 (2021)

Number 4

Non-uniqueness of transonic shock solutions to non-isentropic Euler–Poisson system

Pages: 903 – 917



Ben Duan (School of Mathematics, Dalian University of Technology, Dalian, China)

Na Zhang (School of Mathematics, Dalian University of Technology, Dalian, China)


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.


Euler–Poisson system, non-isentropic, non-uniqueness, transonic shocks

2010 Mathematics Subject Classification

35A02, 35L67, 35Q35

The authors’ research was supported by NSFC No.11871133, No.11671412.

Received 26 April 2020

Accepted 7 November 2020

Published 18 June 2021