Skip to Main content Skip to Navigation
New interface
Theses

Équation des ondes sur les espaces symétriques et localement symétriques de type non compact

Abstract : This thesis is devoted to the study of the wave equation on symmetric and locally symmetric spaces of noncompact type. One of our main results is to obtain pointwise kernel estimates for the wave equation on noncompact symmetric spaces of higher rank. They allow us to prove the dispersive property and to establish the Strichartz inequality for a large family of admissible pairs. We deduce global well-posedness results for the corresponding semilinear wave equation with low regularity initial data. In other words, we extend the results obtained on real hyperbolic spaces to noncompact symmetric spaces of general rank. The other part of our work concerns analysis on locally symmetric spaces. On the one hand, we study the wave and Klein-Gordon equations on certain locally symmetric spaces of rank one. On the other hand, we establish a characterization for the bottom of L2 spectrum of Laplacian on locally symmetric spaces of general rank.
Document type :
Theses
Complete list of metadata

https://tel.archives-ouvertes.fr/tel-03042468
Contributor : ABES STAR :  Contact
Submitted on : Tuesday, April 27, 2021 - 10:11:08 AM
Last modification on : Thursday, October 20, 2022 - 3:54:48 AM

File

104176_ZHANG_2020_archivage.pd...
Version validated by the jury (STAR)

Identifiers

  • HAL Id : tel-03042468, version 2

Collections

Citation

Hong-Wei Zhang. Équation des ondes sur les espaces symétriques et localement symétriques de type non compact. Physique [physics]. Université d'Orléans, 2020. Français. ⟨NNT : 2020ORLE3053⟩. ⟨tel-03042468v2⟩

Share

Metrics

Record views

298

Files downloads

302