Quarterly of Applied Mathematics Quarterly of Applied Mathematics
Online ISSN: 1552-4485 Print ISSN: 0033-569X

     

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
Retrieve article in: PDF

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.

References:

1.
F. Bouchut, A. Mangeney-Castelnau, B. Perthame, and J.-P. Vilotte, A new model of Saint Venant and Savage-Hutter type for gravity driven shallow water flows, preprint.

2.
S. Douady, B. Andreotti, and A. Daerr, On granular surface flow equations, Eur. Phys. J. B 11 (1999), 131-142.

3.
J.-F. Gerbeau and B. Perthame, Derivation of viscous Saint-Venant system for laminar shallow water; numerical validation, Discrete and continuous dynamical system- series B 1, no.1 (2001). MR 1821555 (2001m:76029)

4.
A. Kurganov and D. Levy, Central-upwind schemes for Saint-Venant system, M2AN Math. Model. Numer. Anal. 36 (2002), no. 3, 397-425. MR 1918938 (2003d:76115)

5.
P. D. Lax, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, (1973). MR 0350216 (50:2709)

6.
W.-C. Lien, Hyperbolic Conservation Laws with a moving source, Communication on Pure and Applied Mathematics, Vol. LII, (1999), 1075-1098. MR 1692156 (2000c:35153)

7.
T.-P. Liu, Nonlinear resonance for quasilinear hyperbolic equation, J. Math. Phys. 28 no. 11 (1987), 2593-2602. MR 0913412 (88k:35122)

Similar Articles:

Retrieve articles in Quarterly of Applied Mathematics with MSC (2000): 76B15, 76H05, 35L65

Retrieve articles in all Journals with MSC (2000): 76B15, 76H05, 35L65

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


Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2009 Brown University
Comments: qam-query@ams.org		 AMS Website