| Title:
|
Toward a mathematical analysis for a model of suspension flowing down an inclined plane (English) |
| Author:
|
Matsue, Kaname |
| Author:
|
Tomoeda, Kyoko |
| Language:
|
English |
| Journal:
|
Proceedings of Equadiff 14 |
| Volume:
|
Conference on Differential Equations and Their Applications, Bratislava, July 24-28, 2017 |
| Issue:
|
2017 |
| Year:
|
|
| Pages:
|
349-358 |
| . |
| Category:
|
math |
| . |
| 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)]. (English) |
| Keyword:
|
Hyperbolic conservation law, Riemann problem, shock wave, rarefaction, suspension, dilute approximation |
| MSC:
|
03-06 |
| MSC:
|
35L65 |
| . |
| Date available:
|
2019-09-27T08:20:48Z |
| Last updated:
|
2019-09-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/703057 |
| . |
| Reference:
|
[1] Huppert, H.: Flow and instability of a viscous current down a slope., Nature, 300 427–429, (1982). 10.1038/300427a0 |
| Reference:
|
[2] Lax, P. D.: Hyperbolic system of conservation laws II., Comm. Pure Appl. Math. 10 537–566, (1957). MR 0093653, 10.1002/cpa.3160100406 |
| Reference:
|
[3] Mavromoustaki, A., Bertozzi, A. L.: Hyperbolic systems of conservation laws in gravity-driven, particle-laden thin-film flows., Journal of Engineering Mathematics 88 29–48, (2014). MR 3254624, 10.1007/s10665-014-9688-3 |
| Reference:
|
[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). MR 3018604, 10.1017/jfm.2012.567 |
| Reference:
|
[5] Schecter, S., Marchesin, D., Plohr, B. J.: Structurally stable Riemann solutions., J. Differential Equations 126, no. 2, 303–354, (1996). MR 1383980, 10.1006/jdeq.1996.0053 |
| Reference:
|
[6] Smoller, J.: Shock waves and reaction-diffusion equations., Grundlehren der Mathematischen Wissenschaften (Fundamental Principles of Mathematical Sciences), 258 Vol. 258, Springer-Verlag, New York, second edition, (1994). MR 1301779, 10.1007/978-1-4612-0873-0_14 |
| . |
