Bounded almost global solutions for non hamiltonian semi-linear Klein-Gordon equations with radial data on compact revolution hypersurfaces
Annales de l'Institut Fourier, Volume 56 (2006) no. 5, pp. 1419-1456.

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.

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.

DOI: 10.5802/aif.2217
Classification: 35L70,  58J47
Keywords: Almost global solutions, nonlinear Klein-Gordon equation, radial hypersurfaces
Delort, Jean-Marc 1; Szeftel, Jérémie 2

1 Université Paris-Nord, Institut Galilée UMR CNRS 7539 Laboratoire Analyse Géométrie et Applications 99, Avenue J.-B. Clément 93430 Villetaneuse (France)
2 Princeton University Department of Mathematics Fine Hall, Washington Road Princeton NJ 08544-1000 (USA) and Université Bordeaux 1, UMR CNRS 5466 Mathématiques Appliquées de Bordeaux 351 cours de la Libération 33405 Talence cedex (France)
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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, Volume 56 (2006) no. 5, pp. 1419-1456. doi : 10.5802/aif.2217. http://archive.numdam.org/articles/10.5802/aif.2217/

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