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Starting from the three-dimensional Newtonian and incompress-ible Navier-Stokes equations in a compliant straight vessel, we derive a reduced one-dimensional model by an averaging procedure which takes into consideration the elastic properties of the wall structure. In particular, we neglect terms of the first order with respect to the ratio between the… (More)

- Debora Amadori, Wen Shen
- 2009

In this paper we analyze a set of equations proposed by Hadeler and Kuttler [20], describing the flow of granular matter in terms of the heights of a standing layer and of a moving layer. By a suitable change of variables, the system can be written as a 2 × 2 hy-perbolic system of balance laws, which we study in the one-dimensional case. The system is… (More)

We study a scalar integro-differential conservation law. The equation was first derived in [2] as the slow erosion limit of granular flow. Considering a set of more general erosion functions, we study the initial boundary value problem for which one can not adapt the standard theory of conservation laws. We construct approximate solutions with a fractional… (More)

- Debora Amadori, Wen Shen
- 2009

A boundary value problem We consider the initial-boundary value problem, on the quarter plan {(x, t) : x < 0 , t > 0}, for the system h t − (hp) x = (p − 1)h , p t + (p − 1)h x = 0. The boundary condition above corresponds to assigning the flux of the h variable: the incoming quantity of h is prescribed by the map F (t). The system above arises in the study… (More)

- Debora Amadori, Wen Shen
- 2010

In this paper we study an integro-differential equation that arises in modeling slow erosion of granular flow. We construct piecewise constant approximate solutions, using a front tracing technique. Convergence of the approximate solutions is established through proper a priori estimates, which in turn gives global existence of BV solutions. Furthermore ,… (More)

We consider a hyperbolic system of three conservation laws in one space variable. The system is a model for fluid flow allowing phase transitions; in this case the state variables are the specific volume, the velocity and the mass density fraction of the vapor in the fluid. For a class of initial data having large total variation we prove the global… (More)

The ability of Well-Balanced (WB) schemes to capture very accurately steady-state regimes of non-resonant hyperbolic systems of balance laws has been thoroughly illustrated since its introduction by Greenberg and LeRoux [15] (see also the anterior WB Glimm scheme in [8]). This paper aims at showing, by means of rigorous C 0 t (L 1 x) estimates, that these… (More)

In this paper we prove two global existence results for Hughes' model of pedestrian flows under assumptions that ensures that the traces of the solutions along the turning curve are zero for any positive times.