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V. A. Buchin and G. A. Shaposhnikova, “Flow of Shallow Water with a Periodic System of Jumps over a Vertical Surface,” Doklady Physics, Vol. 54, No. 5, 2009, pp. 248-251. doi:10.1134/S1028335809050073

has been cited by the following article:

• TITLE: Modulation Equations for Roll Waves on Vertically Falling Films of a Power-Law Fluid

  AUTHORS: Abdelaziz Boudlal, Valery Liapidevskii

  KEYWORDS: Power-Law Fluid; Thin Film Flow; Vertical Wall; Modulation Equations; Nonlinear Stability; Roll Wave

  JOURNAL NAME: World Journal of Mechanics, Vol.2 No.1, February 29, 2012

  ABSTRACT: Waves of finite amplitude on a thin layer of non-Newtonian fluid modelled as a power-law fluid are considered. In the long wave approximation, the system of equations taking into account the viscous and nonlinear effects has the hyper- bolic type. For the two-parameter family of periodic waves in the film flow on a vertical wall the modulation equations for nonlinear wave trains are derived and investigated. The stability criterium for roll waves based on the hyperbolicity of the modulation equations is suggested. It is shown that the evolution of stable roll waves can be described by self-similar solutions of the modulation equations.