Buffer phenomenon in the spatially one-dimensional Swift-Hohenberg equation

  • A. Yu. Kolesov
  • E. F. Mishchenko
  • N. Kh. RozovEmail author


We consider a boundary value problem for the spatially one-dimensional Swift-Hohenberg equation with zero Neumann boundary conditions at the endpoints of a finite interval. We establish that as the length l of the interval increases while the supercriticality ɛ is fixed and sufficiently small, the number of coexisting stable equilibrium states in this problem indefinitely increases; i.e., the well-known buffer phenomenon is observed. A similar result is obtained in the 2l-periodic case.


Equilibrium State STEKLOV Institute Solvability Condition Dissipative Structure Instability Domain 
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© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • A. Yu. Kolesov
    • 1
  • E. F. Mishchenko
    • 2
  • N. Kh. Rozov
    • 3
    Email author
  1. 1.Yaroslavl State UniversityYaroslavlRussia
  2. 2.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia
  3. 3.Moscow State UniversityMoscowRussia

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