Buffer phenomenon in the spatially one-dimensional Swift--Hohenberg equation
Informatics and Automation, Differential equations and topology. I, Tome 268 (2010), pp. 137-154
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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.
@article{TRSPY_2010_268_a10,
author = {A. Yu. Kolesov and E. F. Mishchenko and N. Kh. Rozov},
title = {Buffer phenomenon in the spatially one-dimensional {Swift--Hohenberg} equation},
journal = {Informatics and Automation},
pages = {137--154},
publisher = {mathdoc},
volume = {268},
year = {2010},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TRSPY_2010_268_a10/}
}
TY - JOUR AU - A. Yu. Kolesov AU - E. F. Mishchenko AU - N. Kh. Rozov TI - Buffer phenomenon in the spatially one-dimensional Swift--Hohenberg equation JO - Informatics and Automation PY - 2010 SP - 137 EP - 154 VL - 268 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TRSPY_2010_268_a10/ LA - ru ID - TRSPY_2010_268_a10 ER -
%0 Journal Article %A A. Yu. Kolesov %A E. F. Mishchenko %A N. Kh. Rozov %T Buffer phenomenon in the spatially one-dimensional Swift--Hohenberg equation %J Informatics and Automation %D 2010 %P 137-154 %V 268 %I mathdoc %U http://geodesic.mathdoc.fr/item/TRSPY_2010_268_a10/ %G ru %F TRSPY_2010_268_a10
A. Yu. Kolesov; E. F. Mishchenko; N. Kh. Rozov. Buffer phenomenon in the spatially one-dimensional Swift--Hohenberg equation. Informatics and Automation, Differential equations and topology. I, Tome 268 (2010), pp. 137-154. http://geodesic.mathdoc.fr/item/TRSPY_2010_268_a10/