An existence result for a model of granular material with non‐constant density

Article type: Research Article

Authors: Gwiazda, Piotr

Affiliations: Department of Mathematics, Darmstadt University of Technology, Schlossgartenstr. 7, 64289 Darmstadt, Germany E‐mail: gwiazda@mathematik.tu‐darmstadt.de

Note: [] Supported by Sonderforschungsbereich 298.

Abstract: We consider a model developed by Savage and Hutter [17,18], which describes the flow of granular avalanches down a smoothly varying slope. The system consists of two nonstrictly hyperbolic equations for height and momentum. 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. Since the model has a discontinuous source term, a new definition of entropy solution must be introduced.

Journal: Asymptotic Analysis, vol. 30, no. 1, pp. 43-60, 2002