The asymptotical analysis of the mathematical model of the fluid flow in the elastic pipe

Abstract

In this paper the model of the fluid flow in elastic pipe is studied. This model is described by the system of hyperbolic equations. The asymptotic analysis of these equations allows to investigate the conditions of the interaction of waves in the resonance case. The averaged system of integrodifferential equations is constructed to find the uniformly valid asymptotic solution in the long time interval and large interval of the dimensional variable.

Keywords

• asymptotical analysis
• averaging
• interaction of waves
• resonance
• the systems of hyperbolicequations