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1998 Well-posedness of the shallow water equations in the presence of a front
Michael Renardy
Differential Integral Equations 11(1): 95-105 (1998).

Abstract

We consider the initial value problem for the inviscid shallow-water equations in the case where a "front" is present, i.e., a boundary where the fluid depth tends to zero. Since the wave speed in shallow water behaves like the square root of the depth, this results in a degenerate hyperbolic system "on the edge" of change of type. It is shown that smooth solutions exist for smooth initial data.

Citation

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Michael Renardy. "Well-posedness of the shallow water equations in the presence of a front." Differential Integral Equations 11 (1) 95 - 105, 1998.

Information

Published: 1998
First available in Project Euclid: 1 May 2013

zbMATH: 1008.35051
MathSciNet: MR1607996

Subjects:
Primary: 35Q35
Secondary: 35L80, 76B15, 76C05

Rights: Copyright © 1998 Khayyam Publishing, Inc.

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Vol.11 • No. 1 • 1998
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