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

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Abstract

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.

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Authors and Affiliations

  1. Yaroslavl State University, ul. Sovetskaya 14, Yaroslavl, 150000, Russia

    A. Yu. Kolesov

  2. Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    E. F. Mishchenko

  3. Moscow State University, Moscow, 119991, Russia

    N. Kh. Rozov

Authors
  1. A. Yu. Kolesov
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  2. E. F. Mishchenko
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  3. N. Kh. Rozov
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Correspondence to N. Kh. Rozov.

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Original Russian Text © A.Yu. Kolesov, E.F. Mishchenko, N.Kh. Rozov, 2010, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Vol. 268, pp. 137–154.

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Kolesov, A.Y., Mishchenko, E.F. & Rozov, N.K. Buffer phenomenon in the spatially one-dimensional Swift-Hohenberg equation. Proc. Steklov Inst. Math. 268, 130–147 (2010). https://doi.org/10.1134/S0081543810010116

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  • DOI: https://doi.org/10.1134/S0081543810010116

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