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We consider persistence properties of solutions for a generalised wave equation including vibration in elastic rods and shallow water models, such as the BBM, the Dai’s, the Camassa–Holm, and the Dullin–Gottwald–Holm equations, as well as some recent shallow water equations with Coriolis effect. We establish unique continuation results and exhibit asymptotic profiles for the solutions of the general class considered. From these results we prove the non-existence of non-trivial spatially compactly supported solutions for the equation. As an aftermath, we study the equations earlier mentioned in light of our results for the general class. [ABSTRACT FROM AUTHOR]

We extend recently proposed flux globalization based well-balanced path-conservative central-upwind schemes to several shallow water models including the Saint-Vevant system with and without the Manning friction term and rotating shallow water equations. We focus on development of the well-balanced schemes capable of exactly preserving quite complicated steady-state solutions the studied systems admit when the bottom topography is discontinuous. In such cases, nonconservative product terms naturally appear and they require a special treatment. To this end, we incorporate the nonconservative product terms into the global fluxes using the path-conservative technique implemented within a framework of simple—yet highly accurate and robust—Riemann-problem-solver-free central-upwind schemes. This results in new flux globalization based central-upwind schemes, which are more accurate than their existing counterparts. The advantages of the proposed schemes are demonstrated on a number of numerical examples. [ABSTRACT FROM AUTHOR]

We present new models to describe shallow water flows over non smooth topographies. The water waves problem is formulated as a system of two equations on surface quantities in which the topography is involved in a Dirichlet-Neumann operator. Starting from this formulation and using the joint analyticity of this operator with respect to the surface and the bottom parametrizations, we derive a nonlocal shallow water model which only includes smoothing contributions of the bottom. Under additional small amplitude assumptions, Boussinesq-type systems are also derived. Using these alternative shallow water models as references, we finally present numerical tests to assess the precision of the classical shallow water approximations over rough bottoms. In the case of a polygonal bottom, we show numerically that our new model is consistent with the approach developed by Nachbin. [ABSTRACT FROM AUTHOR]