Journal of Dynamics and Differential Equations

, Volume 4, Issue 4, pp 585–615 | Cite as

Global analysis of the phase portrait for the Kuramoto-Sivashinsky equation

  • Ju. S. Il'yashenko


The global behavior of the Kuramoto-Sivashinsky equation is studied. The existence of an absorbing ball in every Sobolev norm is proved. The transition of energy from low modes to high ones is observed. An upper estimate for the Hausdorff dimension of the attractor is given. The main tool is to use the methods of the theory of ordinary differential equations in the investigation of partial differential equations.

Key words

Phase portrait Kuramoto-Sivashinsky equation global analysis 


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Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • Ju. S. Il'yashenko
    • 1
  1. 1.Department of Mathematics and MechanicsMoscow State UniversityMoscowRussia

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