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Tr. Mat. Inst. Steklova, 2010, Volume 268, Pages 137–154 (Mi tm2877)  

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

A. Yu. Kolesova, E. F. Mishchenkob, N. Kh. Rozovc

a Yaroslavl State University, Yaroslavl, Russia
b Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
c Moscow State University, Moscow, Russia

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 $\varepsilon$ 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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English version:
Proceedings of the Steklov Institute of Mathematics, 2010, 268, 130–147

Bibliographic databases:

UDC: 517.926
Received in October 2008

Citation: A. Yu. Kolesov, E. F. Mishchenko, N. Kh. Rozov, “Buffer phenomenon in the spatially one-dimensional Swift–Hohenberg equation”, Differential equations and topology. I, Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin, Tr. Mat. Inst. Steklova, 268, MAIK Nauka/Interperiodica, Moscow, 2010, 137–154; Proc. Steklov Inst. Math., 268 (2010), 130–147

Citation in format AMSBIB
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\by A.~Yu.~Kolesov, E.~F.~Mishchenko, N.~Kh.~Rozov
\paper Buffer phenomenon in the spatially one-dimensional Swift--Hohenberg equation
\inbook Differential equations and topology.~I
\bookinfo Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin
\serial Tr. Mat. Inst. Steklova
\yr 2010
\vol 268
\pages 137--154
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\crossref{https://doi.org/10.1134/S0081543810010116}
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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