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Global Existence of Large BV Solutions in a Model of Granular Flow

Summary: Global Existence of Large BV Solutions
in a 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
January 5, 2009
In this paper we analyze a set of equations proposed by Hadeler and Kuttler [20], de-
scribing 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 linearly degenerate along two straight lines in the phase plane, and therefore is weakly
linearly degenerate at the point of the intersection. The source term is quadratic, consisting
of product of two quantities, which are transported with strictly different speeds. Assuming
that the initial height of the moving layer is sufficiently small, we prove the global existence
of entropy-weak solutions to the Cauchy problem, for a class of initial data with bounded
but possibly large total variation.


Source: Amadori, Debora - Dipartimento di Matematica Pura e Applicata, Universitą dell'Aquila
Conservation Laws
Shen, Wen - Department of Mathematics, Pennsylvania State University


Collections: Mathematics; Physics