Asymptotics of Solutions of the Wave Equation on de Sitter-Schwarzschild Space

被引：34

作者：

Melrose, Richard ^{[1
]}

Barreto, Antonio Sa ^{[2
]}

Vasy, Andras ^{[3
]}

机构：

[1] MIT, Dept Math, Cambridge, MA 02139 USA

[2] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[3] Stanford Univ, Dept Math, Stanford, CA 94305 USA

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2014年 / 39卷 / 03期

基金：

美国国家科学基金会;

关键词：

Asymptotically hyperbolic spaces; Compactification; De Sitter-Schwarzschild space; Exponential decay; Waves; 35L05; 35P25; 83C57; 83C30; LOCAL ENERGY; RESOLVENT; PROPAGATION; SCATTERING; DECAY;

D O I：

10.1080/03605302.2013.866958

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Solutions to the wave equation on de Sitter-Schwarzschild space with smooth initial data on a Cauchy surface are shown to decay exponentially to a constant at temporal infinity, with corresponding uniform decay on the appropriately compactified space.

引用

页码：512 / 529

页数：18

共 16 条

[1] Barreto AS, 1997, MATH RES LETT, V4, P103
[2] Decay and non-decay of the local energy for the wave equation on the De Sitter-Schwarzschild metric
Bony, Jean-Francois
Hafner, Dietrich
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2008, 282 (03) : 697 - 719
[3] Semiclassical resolvent estimates for trapping perturbations
Bruneau, V
Petkov, V
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2000, 213 (02) : 413 - 432
[4] Uniform estimates of the resolvent of the Laplace-Beltrami operator on infinite volume Riemannian manifolds. II
Cardoso, F
Vodev, G
[J]. ANNALES HENRI POINCARE, 2002, 3 (04): : 673 - 691
[5] Dafermos M., PREPRINT
[6] PROPAGATION THROUGH TRAPPED SETS AND SEMICLASSICAL RESOLVENT ESTIMATES
Datchev, Kiril
Vasy, Andras
[J]. ANNALES DE L INSTITUT FOURIER, 2012, 62 (06) : 2347 - 2377
[7] Gluing Semiclassical Resolvent Estimates via Propagation of Singularities
Datchev, Kiril
Vasy, Andras
[J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2012, 2012 (23) : 5409 - 5443
[8] RADIATION-FIELDS AND HYPERBOLIC SCATTERING-THEORY
FRIEDLANDER, FG
[J]. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1980, 88 (NOV) : 483 - 515
[9] Notes on the wave equation on asymptotically Euclidean manifolds
Friedlander, FG
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2001, 184 (01) : 1 - 18
[10] Meromorphic properties of the resolvent on asymptotically hyperbolic manifolds
Guillarmou, C
[J]. DUKE MATHEMATICAL JOURNAL, 2005, 129 (01) : 1 - 37

← 1 2 →