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ÉQUATION DES ONDES SUR LES ESPACES SYMÉTRIQUES RIEMANNIENS DE TYPE NON COMPACT.

Abstract : In this memoir we study evolution equations on curved manifolds. In particular we are interested in the wave equation on Riemannian symmetric spaces of the noncompact type. Dispersive properties of solutions of homogeneous Cauchy problem are proved. These properties are then used to establish Strichartz-type estimates. A closer study of these estimates shows that the nonlinear Cauchy problem with power-like nonlinearities is globally well posed for small initial data and locally well posed for arbitrary initial data. The first chapter is devoted to definitions, algebraic and geometric properties of symmetric spaces and to few elementary aspects of spherical analysis on these spaces. Then our main results are represented in an article : Wave equation on Riemannian symmetric spaces. In the last chapter we present in detail two open problems for future work. One issue is to establish a link between the asymptotic behavior of the estimates and nilpotent orbits, while another issue is the study of wave equation for differential forms on symmetric spaces.
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https://theses.hal.science/tel-00669082
Contributor : Ali Hassani Connect in order to contact the contributor
Submitted on : Saturday, February 11, 2012 - 9:27:25 AM
Last modification on : Thursday, October 21, 2021 - 3:16:05 PM
Long-term archiving on: : Thursday, November 22, 2012 - 12:05:23 PM

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  • HAL Id : tel-00669082, version 1

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Ali Hassani. ÉQUATION DES ONDES SUR LES ESPACES SYMÉTRIQUES RIEMANNIENS DE TYPE NON COMPACT.. Mathématiques générales [math.GM]. Université de Nanterre - Paris X, 2011. Français. ⟨NNT : ⟩. ⟨tel-00669082⟩

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