Integral Equations

Differential Equations

, Volume 48, Issue 9, pp 1258-1271

First online:

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

  • A. N. KulikovAffiliated withYaroslavl State University

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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.