Wave patterns for shallow water equations

Chiu Ya Lan*, Huey Er Lin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)225-249
Number of pages25
JournalQuarterly of Applied Mathematics
Issue number2
Publication statusPublished - 2005 Jun
Externally publishedYes

ASJC Scopus subject areas

  • Applied Mathematics


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