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Some invariant solutions of the Savage-Hutter model for granular avalanches. (English) Zbl 1037.35007

Nikitin, A. G. (ed.) et al., Proceedings of the fourth international conference on symmetry in nonlinear mathematical physics, Kyïv, Ukraine, July 9–15, 2001. Part 1. Dedicated to the 200th anniversary of M. Ostrohrads’kyi. Kyïv: Institute of Mathematics of NAS of Ukraine (ISBN 966-02-2486-9). Proc. Inst. Math. Natl. Acad. Sci. Ukr., Math. Appl. 43(1), 111-119 (2002).
The Savage-Hutter model is considered describing the gravity-driven free surface flow of granular avalanches. This model is described by a time-dependent system of two first order nonlinear equations in one space dimension. All similarity solutions of the system are found, and initial and boundary problems for different profiles of the initial avalanche thickness are studied. The authors plot solutions and discuss their properties depending on parameters of the model.
For the entire collection see [Zbl 0989.00037].

MSC:

35A30 Geometric theory, characteristics, transformations in context of PDEs
35C05 Solutions to PDEs in closed form
35F30 Boundary value problems for nonlinear first-order PDEs
35Q80 Applications of PDE in areas other than physics (MSC2000)
58J70 Invariance and symmetry properties for PDEs on manifolds
76T25 Granular flows
76M60 Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics
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