Preprint 1999-019

Granular Avalanche Flow Down a Smoothly Varying Slope: The Existence of Entropy Solutions

Abstract: We consider a model developed by Savage and Hutter which describes the flow of granular avalanches down a smoothly varying slope. The system of two nonstrictly hyperbolic conservation equations for height and momentum of the avalanche resembles the shallow water equations.

The existence of entropy solutions to this model is proved using the vanishing viscosity method, where we make extensive use of a generalised version of the invariant region theorem in order to prove a priori estimates. Existence can generally only be guaranteed for a finite time depending on the initial data and the geometry of the slope, though in some cases we can say more.

A feature of the model is that it has a discontinuous source term. In order to prove the existence of the viscosity limit, we must also use a monotonicity argument to deal with this term.

Paper:

Available as PostScript.

Author(s):

Robin Balean, <balean@mathematik.tu-darmstadt.de>

Publishing information:

Comments:

This paper is a new version of preprint 1998-040. The discontinuous source term is now handled (rather than a Lipschitz approximation) and better a priori estimates are derived in the constant and steepening slope cases.

Submitted by:

<balean@mathematik.tu-darmstadt.de> June 21 1999.