Stable-range approach to the equation of nonstationary transonic gas flows
Author:
Xiaoping Xu
Journal:
Quart. Appl. Math. 65 (2007), 529-547
MSC (2000):
Primary 35C05, 35Q35; Secondary 35C10, 35C15
DOI:
https://doi.org/10.1090/S0033-569X-07-01057-9
Published electronically:
July 25, 2007
MathSciNet review:
2354886
Full-text PDF Free Access
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Abstract: Using a certain finite-dimensional stable range of the nonlinear terms, we obtain large families of exact solutions parameterized by functions for the equation of nonstationary transonic gas flows discovered by Lin, Reissner and Tsien and its three-dimensional generalization.
References
- N. H. Ibragimov, Lie Group Analysis of Differential Equations, Volume 1, CRC Handbook, CRC Press, 1995.
- C. C. Lin, E. Reissner, and H. S. Tsien, On two-dimensional non-steady motion of a slender body in a compressible fluid, J. Math. Physics. 27 (1948), 220–231. MR 0026499
- P. Kucharczyk, Group properties of the “short waves” equations in gas dynamics, Bull. Acad. Polon. Sci., Ser. Sci. Techn. XIII (1965), no. 5, 469.
- P. Kucharczyk, Teoria Grup Liego w Zastosowaniu do Rówman Rózniczkowych Czaskowych, IPPT Polish Academy of Sciences, Warsaw, 65, 1967.
- E. V. Mamontov, On the theory of nonstationary transonic flows, Dokl. Acad. Nauk SSSR 185 (1969), no. 3, 538.
- E. V. Mamontov, Analytic perturbations in a nonstationary transonic stream, Dinamika Splošn. Sredy Vyp. 10 (1972), 217–222, 249 (Russian). MR 0459234
- O. S. Ryzhov and G. M. Šefter, On unsteady gas flows in Laval nozzles, Soviet Physics. Dokl. 4 (1959), 939–942. MR 0119694
- G. D. Sevost′janov, An equation for nonstationary transonic flows of an ideal gas, Izv. Akad. Nauk SSSR Meh. Židk. Gaza 1 (1977), 105–109 (Russian). MR 0475254
- S. V. Suhinin, A group property and conservation laws of an equation of transonic motion of a gas, Dinamika Sploshn. Sredy 36 Dinamika Zhidkosti so Svobodnymi Granitsami (1978), 130–137, 162 (Russian). MR 539014
References
- N. H. Ibragimov, Lie Group Analysis of Differential Equations, Volume 1, CRC Handbook, CRC Press, 1995.
- C. C. Lin, E. Reissner and H. S. Tsien, On two-dimensional non-steady motion of a slender body in a compressible fluid, J. Math, Phys. 27 (1948), no. 3, 220. MR 0026499 (10:162e)
- P. Kucharczyk, Group properties of the “short waves” equations in gas dynamics, Bull. Acad. Polon. Sci., Ser. Sci. Techn. XIII (1965), no. 5, 469.
- P. Kucharczyk, Teoria Grup Liego w Zastosowaniu do Rówman Rózniczkowych Czaskowych, IPPT Polish Academy of Sciences, Warsaw, 65, 1967.
- E. V. Mamontov, On the theory of nonstationary transonic flows, Dokl. Acad. Nauk SSSR 185 (1969), no. 3, 538.
- E. V. Mamontov, Analytic perturbations in a nonstationary transonic stream, Dinamika Splosn. Sredy Vyp. 10 (1972), 217-222. MR 0459234 (56:17428)
- O. S. Ryzhov and G. M. Shefter, On unsteady gas flows in Laval nozzles, Soviet Physics. Dokl. 4 (1959), 939-942. MR 0119694 (22:10455)
- G. D. Sevost’janov, An equation for nonstationary transonic flows of an ideal gas, Izv. Acad. Nauk SSSR Meh. Zidk. Gaza, 1977, no.1, 105-109. MR 0475254 (57:14871)
- S. V. Sukhinin, Group property and conservation laws of the equation of transonic motion of gas, Dinamika Splosh. Sredi 36 (1978), 130. MR 539014 (80h:76037)
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Additional Information
Xiaoping Xu
Affiliation:
Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China
Received by editor(s):
October 2, 2006
Published electronically:
July 25, 2007
Additional Notes:
Research for this article was supported by China NSF 10431040
Article copyright:
© Copyright 2007
Brown University
