Summary: MATHEMATICAL ASPECTS OF A MODEL FOR
DEBORA AMADORI AND WEN SHEN
Abstract. The model for granular flow being studied by the authors was proposed
by Hadeler and Kuttler in . In one space dimension, by a change of variable, the
system can be written as a 2 × 2 hyperbolic system of balance laws.
Various results are obtained for this system, under suitable assumptions on initial
data which leads to a strictly hyperbolic system. For suitably small initial data, the so-
lution remains smooth globally. Furthermore, the global existence of large BV solutions
for Cauchy problem is established for initial data with small height of moving layer.
Finally, at the slow erosion limit as the height of moving layer tends to zero, the slope of
the mountain provides the unique entropy solution to a scalar integro-differential con-
servation law, implying that the profile of the standing layer depends only on the total
mass of the avalanche flowing downhill.
Various open problems and further research topics related to this model are discussed
at the end of the paper.
Key words. Granular matter, balance laws, weakly linearly degenerate systems,
global large BV solutions, slow erosion.
AMS(MOS) subject classifications. Primary 35L45, 35L50, 35L60, 35L65; Sec-
ondary 35L40, 58J45