Geodesic
Plate braking against the layer of ``delayed'' viscoplastic fluid with regard to wall sliding
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 2, pp. 88-93.

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The paper presents the problem of unstable viscoplastic fluid flow between parallel planes, one of which is fixed, while the other one is put in motion from a standstill under the influence of constant force. Viscoplastic fluid flow develops gradually. The border of the flow is not known in advance and is to be determined in the process of solving the task. The force applied to the upper plate is chosen so as to cause the effect of sliding along the two plates in the course of time. The task definition is given within the limits of five-parameter model, which permits to take up the difference between behavior under stress and without stress as well as possible sliding along the solid walls. Hysteresis of deformation is considered by means of Slibar–Pasly hypothesis. To take the possible sliding along the walls into account, a hypothesis, analogical to the well-known hypothesis for viscous fluid of Prof. N. P. Petrov, is suggested. The offered hypothesis also allows to describe the natural physical condition of smooth transition from “sticking” to “sliding”. Moreover, the parameters included into it can be defined empirically. To solve the task with the required border, a modified method of Kolodner is used. 
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M. I. Safronchik. Plate braking against the layer of ``delayed'' viscoplastic fluid with regard to wall sliding. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 2, pp. 88-93. http://geodesic.mathdoc.fr/item/ISU_2009_9_2_a13/

[1] Slibar A., Paslay P. R., “Retarded Flow of Bingam Materials”, J. of Appl. Mech., 1959 March, 107–112 | MR

[2] Safronchik A. I., Safronchik M. I., “Neustanovivsheesya “zapazdyvayuschee” techenie Kuetta vyazkoplastichnoi sredy mezhdu parallelnymi stenkami”, Matematika. Mekhanika: Sb. nauch. tr., 5, Izd-vo Sarat. un-ta, Saratov, 2003, 177–180

[3] Kolodner J. J., “Free boundary problem for the heat equation wich applications of change of phase”, Com. on Pure and Appl. Math., 9:1 (1956), 1–31 | DOI | MR | Zbl

[4] Safronchik A. I., Nekotorye zadachi neustanovivshegosya techeniya vyazkoplastichnykh sred, Dis. $\dots$ kand. fiz.-mat. nauk, Rostov n/D, 1962, 109 pp.

[5] Sizikov V. S., Smirnov A. V., Fedorov B. A., “Chislennoe reshenie singulyarnogo integralnogo uravneniya Abelya obobschennym metodom kvadratur”, Izv. vuzov. Matematika, 2004, no. 8, 62–70 | MR | Zbl