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Wave patterns for shallow water equations
Author(s):
Chiu-Ya
Lan;
Huey-Er
Lin
Journal:
Quart. Appl. Math.
63
(2005),
225-249.
MSC (2000):
Primary 76B15, 76H05, 35L65
Posted:
April 12, 2005
MathSciNet review:
2150771
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Abstract:
We consider the time-asymptotic behavior of the system of shallow water equations with one bump in one dimension. Our main interest is in the issue of nonlinear stability and instability of the waves, particularly for the transonic flow. In this paper, the formation of the asymptotic wave patterns is done by combining elementary nonlinear waves, shock and rarefaction waves for the conservation laws, and stationary waves. We also describe the bifurcations of the wave patterns as the end states vary.
References:
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- 5.
- P. D. Lax, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, (1973). MR 0350216 (50:2709)
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- 7.
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Additional Information:
Chiu-Ya
Lan
Affiliation:
Institute of Mathematics, Academia Sinica, Nankong, Taipei 11529, Taiwan
Email:
cylan@math.nsysu.edu.tw
Huey-Er
Lin
Affiliation:
Institute of Mathematics, Academia Sinica, Nankong, Taipei 11529, Taiwan
Email:
helin@math.ntnu.edu.tw
PII:
S0033-569X-05-00939-6
Received by editor(s):
April, 2003
Posted:
April 12, 2005
Copyright of article:
Copyright
2005,
Brown University
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