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On measure-valued solutions to a two-dimensional gravity-driven avalanche flow model

✍ Scribed by Piotr Gwiazda

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
196 KB
Volume
28
Category
Article
ISSN
0170-4214

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✦ Synopsis

This paper concerns measure-valued solutions for the two-dimensional granular avalanche ow model introduced by Savage and Hutter. The system is similar to the isentropic compressible Euler equations, except for a Coulomb-Mohr friction law in the source term. We will partially follow the study of measure-valued solutions given by DiPerna and Majda. However, due to the multi-valued nature of the friction law, new more sensitive measures must be introduced. The main idea is to consider the class of x-dependent maximal monotone graphs of non-single-valued operators and their relation with 1-Lipschitz, Carathà eodory functions. This relation allows to introduce generalized Young measures for x-dependent maximal monotone graph.

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