HAL : hal-00698540, version 1

arXiv : 1206.0835

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Schrodinger Equation on homogeneous trees

Alaa Jamal Eddine 1

(16/05/2012)

Let T be a homogeneous tree and L the Laplace operator on T. We consider the semilinear Schrodinger equation associated to L with a power-like nonlinearity F of degree d. We first obtain dispersive estimates and Strichartz estimates with no admissibility conditions. We next deduce global well-posedness for small L2 data with no gauge invariance assumption on the nonlinearity F. On the other hand if F is gauge invariant, L2 conservation leads to global well-posedness for arbitrary L2 data. Notice that, in contrast with the Euclidean case, these global well-posedness results hold with no restriction on d > 1. We finally prove scattering for small L2 data, with no gauge invariance assumption.

1 :	Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO)
	Université d'Orléans – CNRS : UMR7349

Domaine

:

Mathématiques/Théorie des groupes Mathématiques/Equations aux dérivées partielles

Mots Clés : homogeneous tree – nonlinear Schrodinger equation – dispersive estimate – Strichartz estimate – scattering.

hal-00698540, version 1

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Contributeur : Alaa Jamal Eddine <>

Soumis le : Mercredi 16 Mai 2012, 17:01:18

Dernière modification le : Mardi 5 Juin 2012, 09:56:24