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Schrodinger Equation on homogeneous trees

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00698540
Contributor : Alaa Jamal Eddine <>
Submitted on : Wednesday, October 23, 2013 - 10:32:01 AM
Last modification on : Thursday, May 3, 2018 - 3:32:06 PM
Document(s) archivé(s) le : Friday, January 24, 2014 - 4:25:05 AM

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  • HAL Id : hal-00698540, version 2
  • ARXIV : 1206.0835

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Alaa Jamal Eddine. Schrodinger Equation on homogeneous trees. Journal of Lie Theory, 2013, 23 (3), pp.779--794. ⟨hal-00698540v2⟩

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