Bounded almost global solutions for non hamiltonian semi-linear Klein-Gordon equations with radial data on compact revolution hypersurfaces
[Solutions bornées et presque globales pour des équations de Klein-Gordon semilinéaires non hamiltoniennes à données radiales sur des hypersurfaces compactes de révolution]
Delort, Jean-Marc ; Szeftel, Jérémie
Annales de l'Institut Fourier, Tome 56 (2006), p. 1419-1456 / Harvested from Numdam
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Cet article est consacré à la preuve de résultats d’existence presque globale pour des équations de Klein-Gordon sur des hypersurfaces compactes de révolution avec des non-linéarités non hamiltoniennes, lorsque les données sont petites, régulières et radiales. La méthode repose sur l’utilisation de formes normales et sur le fait que les valeurs propres associées à des fonctions propres radiales du Laplacien sont simples et vérifient des propriétés de séparation convenables.

This paper is devoted to the proof of almost global existence results for Klein-Gordon equations on compact revolution hypersurfaces with non-Hamiltonian nonlinearities, when the data are smooth, small and radial. The method combines normal forms with the fact that the eigenvalues associated to radial eigenfunctions of the Laplacian on such manifolds are simple and satisfy convenient asymptotic expansions.

Publié le : 2006-01-01
DOI : https://doi.org/10.5802/aif.2217
Classification:  35L70,  58J47
Mots clés: solutions presque globales, équation non-linéaire de Klein-Gordon, hypersurfaces radiales 
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     author = {Delort, Jean-Marc and Szeftel, J\'er\'emie},
     title = {Bounded almost global solutions for non hamiltonian semi-linear Klein-Gordon equations with radial data on compact revolution hypersurfaces},
     journal = {Annales de l'Institut Fourier},
     volume = {56},
     year = {2006},
     pages = {1419-1456},
     doi = {10.5802/aif.2217},
     zbl = {1115.35084},
     mrnumber = {2273861},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2006__56_5_1419_0}
}

Delort, Jean-Marc; Szeftel, Jérémie. Bounded almost global solutions for non hamiltonian semi-linear Klein-Gordon equations with radial data on compact revolution hypersurfaces. Annales de l'Institut Fourier, Tome 56 (2006) pp. 1419-1456. doi : 10.5802/aif.2217. http://gdmltest.u-ga.fr/item/AIF_2006__56_5_1419_0/

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