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A Hyperbolic Model of Granular Flow Debora Amadori
 

Summary: A Hyperbolic Model of Granular Flow
Debora Amadori
and Wen Shen
(*): Dipartimento di Matematica Pura ed Applicata, University of L'Aquila, Italy.
Email: amadori@univaq.it
(**): Department of Mathematics, Penn State University, U.S.A..
Email: shen w@math.psu.edu
Abstract
In this paper we review some recent results for a model for granular flow that was proposed
by Hadeler & Kuttler in [18], which has recently raised a lot of attention.
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. The known theory applies to the Cauchy problem for this system, as for
instance in the context of small C1
data or small BV data. Moreover, due to the special
hyperbolicity properties of the system and of the special form of the source term, it is possible
to enlarge the class of initial data for which global in time solutions exist. See [2, 27].
Further, we study the "slow erosion/deposition limit", [3], where the thickness of the
moving layer vanishes but the total mass of flowing down material remains positive. The
limiting behavior for the slope of the mountain profile provides an entropy solution to a

  

Source: Amadori, Debora - Dipartimento di Matematica Pura e Applicata, Universitą dell'Aquila

 

Collections: Mathematics