Debora Amadori

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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)
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)
Starting from the three-dimensional Newtonian and incompressible 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)
In this paper we study an integro-differential equation describing slow erosion, in a model of granular flow. In this equation the flux is non local and depends on x, t. We define approximate solutions by using a front tracking technique, adapted to this special equation. Convergence of the approximate solutions is established by means of suitable a priori(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 t (L x ) estimates, that these(More)
In this paper we review some recent results for a model for granular flow that was proposed by Hadeler & Kuttler in [20]. In one space dimension, this model can be written as a 2 × 2 hyperbolic system of balance laws, in which the unknowns represent the thickness of the moving layer and the one of the resting layer. If the slope does not change its sign,(More)