| Type de publication : |
 |
Preprint, Working Paper, Document sans référence, etc. |
|
| Domaine : |
|
|
|
| Titre : |
|
Schrodinger Equation on homogeneous trees |
|
| Auteur(s) : |
|
Alaa Jamal Eddine ( ) 1 |
|
| Laboratoire : |
|
|
|
| Résumé : |
|
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. |
|
Langue du texte
intégral : |
|
Anglais |
|
|
| Mots Clés : |
|
homogeneous tree – nonlinear Schrodinger equation – dispersive estimate – Strichartz estimate – scattering. |
|
| Classification : |
|
35Q55, 43A90, 22E35, 43A85, 81Q05, 81Q35, 35R02 |
|
| Commentaire : |
|
14 pages, 1 figure |
|
|
Récupérer au format
