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Article

Matsue, Kaname ; Tomoeda, Kyoko
Toward a mathematical analysis for a model of suspension flowing down an inclined plane. (English). In: Mikula, Karol (ed.): Proceedings of Equadiff 14. Conference on Differential Equations and Their Applications, Bratislava, July 24-28, 2017. Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing, Bratislava, 2017. pp. 349-358
MSC: 03-06, 35L65
Keywords:
Hyperbolic conservation law, Riemann problem, shock wave, rarefaction, suspension, dilute approximation
Summary:
We consider the Riemann problem of the dilute approximation equations with spatiotemporally dependent volume fractions from the full model of suspension, in which the particles settle to the solid substrate and the clear liquid film flows over the sediment [Murisic et al., J. Fluid. Mech. 717, 203–231 (2013)]. We present a method to find shock waves, rarefaction waves for the Riemann problem of this system. Our method is mainly based on [Smoller, Springer-Verlag, New York, second edition, (1994)].
References:
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[4] HASH(0x18aeb08): [4] N. Murisic, B. Pausader, D. Peschka, A. L. Bertozzi, //Dynamics of particle settling and resuspension in viscous liquids/, J. Fluid Mech. 717 203–231, (2013). DOI 10.1017/jfm.2012.567 | MR 3018604
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