Geodesic
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/}
}
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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/