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

Peletier, Lambertus A.1 ; Rottschäfer, Vivi2
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, Tome 336 (2003) no. 3, pp. 225-230.

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 :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00021-9
Peletier, Lambertus A. 1 ; Rottschäfer, Vivi 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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Peletier, Lambertus A.; Rottschäfer, Vivi. Large time behaviour of solutions of the Swift–Hohenberg equation. Comptes Rendus. Mathématique, Tome 336 (2003) no. 3, pp. 225-230. doi : 10.1016/S1631-073X(03)00021-9. http://www.numdam.org/articles/10.1016/S1631-073X(03)00021-9/

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