Differential Equations

, Volume 48, Issue 9, pp 1258–1271

Landau-Hopf scenario of passage to turbulence in some problems of elastic stability theory

Authors

  • A. N. Kulikov
    • Yaroslavl State University
Integral Equations

DOI: 10.1134/S0012266112090066

Cite this article as:
Kulikov, A.N. Diff Equat (2012) 48: 1258. doi:10.1134/S0012266112090066

Abstract

We consider a boundary value problem for a nonlinear integro-differential equation modeling the vibrations of a pipe transporting a fluid and the vibrations of a thin cylinder in an axisymmetric flow. For the boundary conditions we take the hinge support conditions. We show that the Landau-Hopf scenario of passage to turbulence can be realized in such a problem, whereby stable invariant tori of increasing dimensions are generated as the main bifurcation parameter increases.

Copyright information

© Pleiades Publishing, Ltd. 2012