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Problème mixte hyperbolique avec saut sur la condition aux limites

Jean-Marc Delort — 1989

Annales de l'institut Fourier

Ce travail est consacré à l’étude du problème mixte linéaire pour un système N × N non caractéristique, strictement hyperbolique, de degré 1, dans le cas où la condition aux limites présente un saut sur une hypersurface non caractéristique du bord. Sous la condition de Lopatinski uniforme hors de cette hypersurface et sous une hypothèse supplémentaire le long de celle-ci, on prouve un résultat d’existence et d’unicité dans l’espace de Sobolev H ν ν 0 , 1 2 . On étudie ensuite la propagation de la régularité conormale...

Normal Forms and Long Time Existence for Semi-Linear Klein-Gordon Equations

Jean-Marc Delort — 2007

Bollettino dell'Unione Matematica Italiana

We present in this text two results of long time existence for solutions of nonlinear Klein-Gordon equations, obtained through normal forms methods. In particular, we indicate how these methods allow one to obtain almost global solutions for that equation on spheres, despite the fact that such solutions do not go to zero when time goes to infinity.

Bounded almost global solutions for non hamiltonian semi-linear Klein-Gordon equations with radial data on compact revolution hypersurfaces

Jean-Marc DelortJérémie Szeftel — 2006

Annales de l’institut Fourier

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.

Almost global solutions for non hamiltonian semi-linear Klein-Gordon equations on compact revolution hypersurfaces

Jean-Marc DelortJérémie Szeftel — 2005

Journées Équations aux dérivées partielles

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.

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