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Instability and reformation of regular waves in falling film of a viscous liquid. (English. Russian original) Zbl 1014.76023
Mosc. Univ. Mech. Bull. 55, No. 4, 19-23 (2000); translation from Vestn. Mosk. Univ., Ser. I 2000, No. 4, 44-48 (2000).
The paper deals with the system of evolutionary equations in the form \(\frac{\partial h}{\partial t} +\frac{\partial q}{\partial x} = 0,\) \(\frac{\partial q}{\partial t} + \frac 65 \frac{\partial}{\partial x}\big(\frac 1{5\delta}\big) = \frac 1{5\delta}\big(h \frac{\partial^3 h}{\partial x^3} + h - \frac{q}{h^2}\big)\) which was studied earlier in [V. Ya. Shkadov, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza 1, 43-50 (1967)]. The authors show that attractive properties of dominating waves are presented also in the case when the initial data are chosen in a small neighborhood of other regular waves.

76E17 Interfacial stability and instability in hydrodynamic stability
76M22 Spectral methods applied to problems in fluid mechanics
76D99 Incompressible viscous fluids