Large time behaviour of solutions of the Swift–Hohenberg equation

Lambertus A. Peletier; Vivi Rottschäfer

doi:10.1016/S1631-073X(03)00021-9

Partial Differential Equations

Large time behaviour of solutions of the Swift–Hohenberg equation
[Comportement des solutions de l'équation de Swift–Hohenberg en grand temps]

Présenté par : Haïm Brezis

Lambertus A. Peletier ¹ ; Vivi Rottschäfer ²

¹ Mathematical Institute, Leiden University, PB 9512, 2300 RA Leiden & Centrum voor Wiskunde en Informatica, PB 94079, 1090 GB Amsterdam, The Netherlands
² Mathematical Institute, Leiden University, PB 9512, 2300 RA Leiden, The Netherlands

Comptes Rendus. Mathématique, Volume 336 (2003) no. 3, pp. 225-230.

Résumé
Abstract

Nous étudions les limites des profiles v des solutions de l'équation Swift–Hohenberg dans une domaine de dimension un (0,L), pour différents choix de L. Nous identifions les valeurs de L pour lesquelles v=0 et nous derivons des estimations pour la taille et la forme quand v minimise une fonctionnelle associée.

We study the limiting profiles v of solutions of the Swift–Hohenberg equation on a one-dimensional domain (0,L) for different values of L. We identify those values of L for which v=0, and discuss the size and the shape of v when it is nontrivial and a global minimiser of an associated energy functional.

Reçu le : 2002-11-27
Accepté le : 2002-12-10
Publié le : 2003-02-01

DOI : 10.1016/S1631-073X(03)00021-9

Affiliations des auteurs :

Lambertus A. Peletier ¹ ; Vivi Rottschäfer ²

¹ Mathematical Institute, Leiden University, PB 9512, 2300 RA Leiden & Centrum voor Wiskunde en Informatica, PB 94079, 1090 GB Amsterdam, The Netherlands
² Mathematical Institute, Leiden University, PB 9512, 2300 RA Leiden, The Netherlands

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     title = {Large time behaviour of solutions of the {Swift{\textendash}Hohenberg} equation},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {225--230},
     publisher = {Elsevier},
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     number = {3},
     year = {2003},
     doi = {10.1016/S1631-073X(03)00021-9},
     language = {en},
}

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Lambertus A. Peletier; Vivi Rottschäfer. Large time behaviour of solutions of the Swift–Hohenberg equation. Comptes Rendus. Mathématique, Volume 336 (2003) no. 3, pp. 225-230. doi : 10.1016/S1631-073X(03)00021-9. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00021-9/

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