In this work, a shallow-water system for interfacial waves in the case of a neutrally buoyant
two-layer fluid system is considered. Such a situation arises in the case of large underwater …

In this paper, we derive asymptotic models for the propagation of two-and three-dimensional
gravity waves at the free surface and the interface between two layers of immiscible fluids of …

We consider the Riemann problem for the system of shallow water equations with horizontal
temperature gradients (the Ripa system). The model under investigation has the form of a …

The Riemann problem of one dimensional shallow water equations with discontinuous
topography has been constructed recently. The elementary waves include shock waves …

In this paper, we consider the Riemann problem and interaction of elementary waves for a
nonlinear hyperbolic system of conservation laws that arises in shallow water theory. This …

Motivated by a new kind of initial boundary value problem (IBVP) with a free boundary
arising in wave-structure interaction, we propose here a general approach to one …

We construct the solution of the Riemann problem for the shallow water equations with
discontinuous topography. The system under consideration is non-strictly hyperbolic and …

In a recent paper LeFloch and Thanh (2011) constructed the Riemann solutions for shallow
water equations with discontinuous topography, where the stationary wave is determined by …

Consideration is given to the shallow-water equations, a hyperbolic system modeling the
propagation of long waves at the surface of an incompressible inviscible fluid of constant …

In this thesis, we investigate the problem of density stratified interfacial flows of immiscible
fluids in the shallow water limit. We focus our attention on the two-and-a-halfand three-layer …