Uniqueness and instability of subsonic–sonic potential flow in a convergent approximate nozzle
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- by Pan Liu and Hairong Yuan PDF
- Proc. Amer. Math. Soc. 138 (2010), 1793-1801 Request permission
Abstract:
We proved uniqueness and instability of the symmetric subsonic–sonic flow solution of the compressible potential flow equation in a surface with convergent areas of cross–sections. Such a surface may be regarded as an approximation of a two–dimensional convergent nozzle in aerodynamics. Mathematically these are uniqueness and nonexistence results of a nonlinear degenerate elliptic equation with Bernoulli type boundary conditions. The proof depends on maximum principles and a generalized Hopf boundary point lemma which was proved in the paper.References
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Additional Information
- Pan Liu
- Affiliation: Department of Mathematics, East China Normal University, Shanghai 200241, People’s Republic of China
- Email: pliu@math.ecnu.edu.cn
- Hairong Yuan
- Affiliation: Department of Mathematics, East China Normal University, Shanghai 200241, People’s Republic of China
- Email: hryuan@math.ecnu.edu.cn, hairongyuan0110@gmail.com
- Received by editor(s): April 27, 2009
- Received by editor(s) in revised form: September 14, 2009, and September 14, 2009
- Published electronically: January 7, 2010
- Additional Notes: The first author was supported in part by the National Science Foundation of China under Grants No. 10601017 and 10871126.
The second author (corresponding author) was supported in part by the National Science Foundation of China under Grant No. 10901052, Shanghai Chenguang Program (09CG20), a Special Research Fund for Selecting Excellent Young Teachers of the Universities in Shanghai sponsored by the Shanghai Municipal Education Commission, and the National Science Foundation (USA) under Grant DMS-0720925. - Communicated by: Walter Craig
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 1793-1801
- MSC (2010): Primary 35J70, 35B50; Secondary 76H05
- DOI: https://doi.org/10.1090/S0002-9939-10-10202-0
- MathSciNet review: 2587464