WAVE AND KLEIN-GORDON EQUATIONS ON HYPERBOLIC SPACES

被引：25

作者：

Anker, Jean-Philippe ^{[1
,2
,3
]}

Pierfelice, Vittoria ^{[1
,2
,3
]}

机构：

[1] Univ Orleans, Federat Denis Poisson FR 2964, F-45067 Orleans 2, France

[2] Univ Orleans, Lab MAPMO UMR 7349, F-45067 Orleans 2, France

[3] CNRS, F-45067 Orleans 2, France

来源：

ANALYSIS & PDE | 2014年 / 7卷 / 04期

关键词：

hyperbolic space; wave kernel; semilinear wave equation; semilinear Klein-Gordon equation; dispersive estimate; Strichartz estimate; global well-posedness; GLOBAL-SOLUTIONS; SCHRODINGER; SCATTERING; EXISTENCE;

D O I：

10.2140/apde.2014.7.953

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Klein-Gordon equation associated with the Laplace-Beltrami operator Delta on real hyperbolic spaces of dimension n >= 2; as Delta has a spectral gap, the wave equation is a particular case of our study. After a careful kernel analysis, we obtain dispersive and Strichartz estimates for a large family of admissible couples. As an application, we prove global well-posedness results for the corresponding semilinear equation with low regularity data.

引用

页码：953 / 995

页数：43

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