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
Michael Renardy. "Well-posedness of the shallow water equations in the presence of a front." Differential Integral Equations 11 (1) 95 - 105, 1998. https://doi.org/10.57262/die/1367414137
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