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Non-uniqueness of transonic shock solutions to non-isentropic Euler-Poisson system. (English) Zbl 1479.35008

Summary: 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 [T. Luo and Z. Xin, ibid. 10, No. 2, 419–462 (2012; Zbl 1286.35165)]. Moreover, the monotonicity with a threshold between the location of the transonic shock and the density at the exit of the nozzle is established.

MSC:

35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
35L67 Shocks and singularities for hyperbolic equations
35Q31 Euler equations
35Q35 PDEs in connection with fluid mechanics

Citations:

Zbl 1286.35165
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