no. 2
Partial Differential Equations
On the global attraction to solitary waves for the Klein–Gordon equation coupled to a nonlinear oscillator
[Attraction globale vers des ondes solitaires pour l'équation de Klein–Gordon couplé à un oscillateur non linéaire]

Présenté par : Pierre-Louis Lions

Komech, Alexander I.1 ; Komech, Andrew A.2
1 Faculty of Mathematics, Vienna University, A-1090 Vienna, Austria
2 Mathematics Department, Texas A&M University, College Station, TX, USA
Comptes Rendus. Mathématique, Tome 343 (2006) no. 2, pp. 111-114.

On s'intéresse aux solutions d'énergie finie d'une équation non linéaire de Klein–Gordon U(1)-invariante monodimensionnelle, avec une non linéarité ponctuelle, et on analyse leur comportement asymptotique aux temps longs. Le principal résultat que nous avons obtenu est que toute solution d'énergie finie converge pour t→±∞ vers un ensemble de « fonctions propres non linéaires » ψ(x)e−iωt.

The long-time asymptotics are analyzed for all finite energy solutions to a model U(1)-invariant nonlinear Klein–Gordon equation in one dimension, with the nonlinearity concentrated at a point. Our main result is that each finite energy solution converges as t→±∞ to the set of ‘nonlinear eigenfunctions’ ψ(x)e−iωt.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.06.009
Komech, Alexander I. 1 ; Komech, Andrew A. 2

1 Faculty of Mathematics, Vienna University, A-1090 Vienna, Austria
2 Mathematics Department, Texas A&M University, College Station, TX, USA 
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Komech, Alexander I.; Komech, Andrew A. On the global attraction to solitary waves for the Klein–Gordon equation coupled to a nonlinear oscillator. Comptes Rendus. Mathématique, Tome 343 (2006) no. 2, pp. 111-114. doi : 10.1016/j.crma.2006.06.009. http://www.numdam.org/articles/10.1016/j.crma.2006.06.009/

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