Uniqueness of transonic shock solutions in a duct for steady potential flow

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:247

Article

Chen, Gui-Qiang^1,2  Yuan, Hairong³ 

[1] Northwestern Univ, Dept Math, Evanston, IL 60208 USA

[2] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[3] E China Normal Univ, Dept Math, Shanghai 200241, Peoples R China

关键词: Uniqueness;    Transonic shock;    Free boundary;    Bernoulli law;    Maximum principle;    Potential flow;    Duct;   

DOI  :  10.1016/j.jde.2008.11.016

来源: Elsevier

【 摘 要 】

We study the uniqueness of solutions with a transonic shock in a duct in a class of transonic shock solutions, which are not necessarily small perturbations of the background solution, for steady potential flow. We prove that, for given uniform supersonic upstream flow in a straight duct, there exists a unique uniform pressure at the exit of the duct such that a transonic shock solution exists in the duct, which is unique modulo translation. For any other given uniform pressure at the exit, there exists no transonic shock solution in the duct. This is equivalent to establishing a uniqueness theorem for a free boundary problem of a partial differential equation of second order in a bounded or unbounded duct. The proof is based on the maximum/comparison principle and a judicious choice of special transonic shock solutions as a comparison solution. (C) 2008 Published by Elsevier Inc.

【 授权许可】

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