Geodesic
On stability of one-dimensional movement of viscous material
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2020), pp. 86-90

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One-dimensional movement of tensioned viscous material stream is considered. Applying the laws of a mass and motion quantity conservation it is shown, that the stationary flow is characterised by exponential decrease of stream width and corresponding increase of stream velocity. Equations for perturbations of station variables are derived, which depend on the defining parameter. This parameter characterises the combined influence of viscosity, density, initial velocity and length of the considered interval. For small parameter values dynamic stability of one-dimensional material motion is established.
Keywords: moving material, viscosity, stability. 
@article{IVM_2020_10_a7,
     author = {N. V. Banichuk and S. Yu. Ivanova and V. S. Afanas'ev},
     title = {On stability of one-dimensional movement of viscous material},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {86--90},
     publisher = {mathdoc},
     number = {10},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_10_a7/}
}
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N. V. Banichuk; S. Yu. Ivanova; V. S. Afanas'ev. On stability of one-dimensional movement of viscous material. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2020), pp. 86-90. http://geodesic.mathdoc.fr/item/IVM_2020_10_a7/