Ill and well-posed models of granular flow

Harris, D. (2001) Ill and well-posed models of granular flow. Acta Mechanica, 146 (3-4). pp. 199-225. ISSN 1619-6937

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Abstract

A unified method of generating models for the flow of granular materials is used to confirm and extend the results of Schaeffer and co-workers [15], [17]–[19], namely that many existing models exhibit linear ill-posedness with regard to initial conditions. A model proposed in Harris [6], [7] is analyzed by the same method and it is established that, firstly, the model exhibits well-posedness under certain well-defined conditions, secondly, that when these conditions fail to hold, the model exhibits ill-posedness and thirdly, the mathematical ill-posedness corresponds to a real physical instability.

Item Type:	Article
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations MSC 2010, the AMS's Mathematics Subject Classification > 70 Mechanics of particles and systems MSC 2010, the AMS's Mathematics Subject Classification > 74 Mechanics of deformable solids
Depositing User:	Ms Lucy van Russelt
Date Deposited:	12 Jul 2006
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/372

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