CORRADO MASCIA

A dive into shallow water

Pages: 77-149
Received: 1 February 2010   
Accepted: 22 June 2010
Mathematics Subject Classification (2000): 76-01, 35Q35, 76B15, 82C40.

Keywords: Shallow water equations, hyperbolic-parabolic systems, roll-waves, kinetic equations.

Abstract: In this tutorial, we attempt to furnish a basic introduction on shallow water modeling with specific attention to Saint-Venant equations. We propose a selection of results, including derivation of the model, well-posedness of the Cauchy problem, existence and stability of roll-waves, kinetic formulation and the corresponding hydrodynamical limit, presented, whenever possible, in a simplified way and designed mainly for readers that are not expert in the field.