Wave patterns for shallow water equations

Chiu Ya Lan; Huey Er Lin

doi:10.1090/S0033-569X-05-00939-6

Wave patterns for shallow water equations

Chiu Ya Lan^*, Huey Er Lin

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	225-249
Number of pages	25
Journal	Quarterly of Applied Mathematics
Volume	63
Issue number	2
DOIs	https://doi.org/10.1090/S0033-569X-05-00939-6
Publication status	Published - 2005 Jun
Externally published	Yes

ASJC Scopus subject areas

Applied Mathematics

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10.1090/S0033-569X-05-00939-6

Cite this

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author = "Lan, {Chiu Ya} and Lin, {Huey Er}",

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AB - 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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Wave patterns for shallow water equations

Abstract

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