Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Wave patterns for shallow water equations

Authors: Chiu-Ya Lan and Huey-Er Lin
Journal: Quart. Appl. Math. 63 (2005), 225-249
MSC (2000): Primary 76B15, 76H05, 35L65
DOI: https://doi.org/10.1090/S0033-569X-05-00939-6
Published electronically: April 12, 2005
MathSciNet review: 2150771
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Abstract | References | Similar Articles | Additional Information

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.

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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

DOI: https://doi.org/10.1090/S0033-569X-05-00939-6
Received by editor(s): April 1, 2003
Published electronically: April 12, 2005
Article copyright: © Copyright 2005 Brown University

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