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, p. 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 : https://doi.org/10.5802/aif.2217
Classification:  35L70,  58J47
Keywords: Almost global solutions, nonlinear Klein-Gordon equation, radial hypersurfaces
@article{AIF_2006__56_5_1419_0,
     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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {56},
     number = {5},
     year = {2006},
     pages = {1419-1456},
     doi = {10.5802/aif.2217},
     mrnumber = {2273861},
     zbl = {1115.35084},
     language = {en},
     url = {http://www.numdam.org/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, Volume 56 (2006) no. 5, pp. 1419-1456. doi : 10.5802/aif.2217. http://www.numdam.org/item/AIF_2006__56_5_1419_0/

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