超音速流越过弯曲坡面的反问题

数学物理学报 ›› 2018, Vol. 38 ›› Issue (4): 679-686.

超音速流越过弯曲坡面的反问题

王丽

上海电机学院文理教学部上海 201306

收稿日期:2017-02-20 修回日期:2017-10-20 出版日期:2018-08-26 发布日期:2018-08-26
作者简介:王丽,E-mail:wangli@sdju.edu.cn
基金资助:
上海电机学院学科建设项目（16JCXK02）

The Inverse Problem for the Supersonic Plane Flow Past a Curved Wedge

Wang Li

Department of Mathematics and Physics, Shanghai Dianji University, Shanghai 201306

Received:2017-02-20 Revised:2017-10-20 Online:2018-08-26 Published:2018-08-26
Supported by:
Supported by Academic Discipline Project of Shanghai Dianji University (16JCXK02)

摘要/Abstract

摘要： 该文研究由TSD方程刻画的超音速流越过弯曲坡面的反问题.该文将确定一个弯曲的坡面，使得超音速流越过它时产生的激波在给定的位置.这类问题在航空工业领域应用广泛.在合适的假设条件下，运用黎曼不变量和Lax变换，通过解一个广义柯西问题，该文得到上述问题解的整体存在性及唯一性.

关键词: TSD方程, 黎曼不变量, Lax变换, 广义柯西问题

Abstract: The inverse problem for the supersonic plane flow described by TSD equation past a curved wedge is considered. For a uniform supersonic oncoming flow, under the hypothesis that the position of the shock is given, we will globally determine the curved wedge. This kind of problem plays an important role in the aviation industry. Under suitable assumptions, with the help of Riemann invariants and Lax transform, by solving a generalized Cauchy problem, the global existence and uniqueness for the above mentioned problem is established.

Key words: TSD equation, Riemann invariants, Lax transform, Generalized Cauchy problem

中图分类号:

O175.27

王丽. 超音速流越过弯曲坡面的反问题[J]. 数学物理学报, 2018, 38(4): 679-686.

Wang Li. The Inverse Problem for the Supersonic Plane Flow Past a Curved Wedge[J]. Acta mathematica scientia,Series A, 2018, 38(4): 679-686.