Almost global solutions for non hamiltonian semi-linear Klein-Gordon equations on compact revolution hypersurfaces
Journées équations aux dérivées partielles (2005), article no. 15, 13 p.

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.

DOI : 10.5802/jedp.26
Classification : 35L70, 34L20
Mots clés : almost global existence, nonlinear Klein-Gordon equation, revolution hypersurfaces, normal forms
Delort, Jean-Marc 1 ; Szeftel, Jérémie 2

1 Laboratoire Analyse Géométrie et Applications, UMR CNRS 7539 Institut Galilée, Université Paris-Nord, 99, Avenue J.-B. Clément, F-93430 Villetaneuse FRANCE
2 Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton NJ 08544-1000 USA and Mathématiques Appliquées de Bordeaux, UMR CNRS 5466, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence cedex FRANCE
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Delort, Jean-Marc; Szeftel, Jérémie. Almost global solutions for non hamiltonian semi-linear Klein-Gordon equations on compact revolution hypersurfaces. Journées équations aux dérivées partielles (2005), article  no. 15, 13 p. doi : 10.5802/jedp.26. http://www.numdam.org/articles/10.5802/jedp.26/

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