Sur le comportement des solutions d’équations de Schrödinger non linéaires à croissance exponentielle
Séminaire Laurent Schwartz — EDP et applications (2014-2015), Exposé no. 10, 11 p.

On se propose dans cet exposé de décrire le comportement des solutions de l’équation de Schrödinger non linéaire à croissance exponentielle, où la norme d’Orlicz joue un rôle crucial. Notre analyse qui est basée sur les décompositions en profils met en lumière le rôle distingué de la composante 1-oscillante de la suite des données initiales. Ce phénomène est complètement différent de ceux obtenus dans le cadre des équations semi-linéaires dispersives critiques, où toutes les composantes oscillantes créent le même effet non linéaire, à un changement d’échelle près.

@article{SLSEDP_2014-2015____A10_0,
     author = {Bahouri, Hajer},
     title = {Sur le comportement des solutions d{\textquoteright}\'equations de Schr\"odinger non lin\'eaires \`a croissance exponentielle},
     journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
     note = {talk:10},
     publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2014-2015},
     doi = {10.5802/slsedp.69},
     language = {fr},
     url = {http://archive.numdam.org/articles/10.5802/slsedp.69/}
}
Bahouri, Hajer. Sur le comportement des solutions d’équations de Schrödinger non linéaires à croissance exponentielle. Séminaire Laurent Schwartz — EDP et applications (2014-2015), Exposé no. 10, 11 p. doi : 10.5802/slsedp.69. http://archive.numdam.org/articles/10.5802/slsedp.69/

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