Mixed type equations in gas dynamics
Author:
Shuxing Chen
Journal:
Quart. Appl. Math. 68 (2010), 487-511
MSC (2000):
Primary 35L65; Secondary 35L67
DOI:
https://doi.org/10.1090/S0033-569X-2010-01164-9
Published electronically:
May 21, 2010
MathSciNet review:
2676973
Full-text PDF Free Access
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Abstract: The paper is mainly concerned with mixed type partial differential equations and their connections with transonic flow. Some typical problems in gas dynamics related to the mixed type equations are presented and analyzed. In the meantime, the crucial points on the study of these problems, including some recent developments and new approaches, are introduced.
References
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- S. X. Chen, A singular multi-dimensional piston problem in compressible flow. Jour. Diff. Eqs. 189 (2003), 292-317. MR 1968323 (2004d:76084)
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- T. P. Liu, Nonlinear stability and instability of transonic flows through a nozzle. Comm. Math. Phys. 83 (1982), 243-260. MR 649161 (83f:35014)
- T. P. Liu, Transonic gas flows in a variable area duct. Arch. Rat. Mech. Anal. 80 (1982), 1-18. MR 656799 (83h:76050)
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- C. S. Morawetz, Potential theory for regular and Mach reflection of a shock at a wedge, Comm. Pure Appl. Math. 47 (1994), 593-624. MR 1278346 (95g:76030)
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Additional Information
Shuxing Chen
Affiliation:
School of Mathematical Sciences, Fudan University, Shanghai, 200433, People’s Republic of China
Email:
sxchen@public8.sta.net.cn
Keywords:
Mixed type equation,
Tricomi equation,
Keldysh equation,
Lavrentiev equation,
transonic flow,
Mach configuration
Received by editor(s):
November 20, 2008
Published electronically:
May 21, 2010
Article copyright:
© Copyright 2010
Brown University
The copyright for this article reverts to public domain 28 years after publication.