Global solutions for semilinear Klein-Gordon equations in FLRW spacetimes

被引：34

作者：

Galstian, Anahit ^{[1
]}

Yagdjian, Karen ^{[1
]}

机构：

[1] Univ Texas Pan Amer, Dept Math, Edinburg, TX 78539 USA

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2015年 / 113卷

关键词：

Klein-Gordon equation; Einstein-de Sitter universe; de Sitter universe; Global solutions; SITTER SPACETIME; FUTURE STABILITY; CAUCHY-PROBLEM; SCALAR FIELD; EXISTENCE; SYSTEM;

D O I：

10.1016/j.na.2014.10.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider waves, which obey the semilinear Klein-Gordon equation, propagating in the Friedmann-Lema (i) over cap tre-Robertson-Walker spacetimes. The equations in the de Sitter and Einstein-de Sitter spacetimes are the important particular cases. We show the global in time existence in the energy class of solutions of the Cauchy problem. (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：339 / 356

页数：18

共 18 条

[1] Strichartz Estimates on Asymptotically de Sitter Spaces [J].

Baskin, Dean .

ANNALES HENRI POINCARE, 2013, 14 (02) :221-252

[2] A parametrix for the fundamental solution of the Klein-Gordon equation on asymptotically de Sitter spaces [J].

Baskin, Dean .

JOURNAL OF FUNCTIONAL ANALYSIS, 2010, 259 (07) :1673-1719

[3] Global wave maps on Robertson-Walker spacetimes [J].

Choquet-Bruhat, Y .

NONLINEAR DYNAMICS, 2000, 22 (01) :39-47

[4]

Choquet-Bruhat Y., 2009, OXFORD MATH MONOGRAP

[5]

Hawking S. W., 1973, CAMBRIDGE MONOGRAPHS, V1

[6] FORBIDDEN MASS RANGE FOR SPIN-2 FIELD-THEORY IN DESITTER SPACETIME [J].

HIGUCHI, A .

NUCLEAR PHYSICS B, 1987, 282 (02) :397-436

[7]

Hintz P., ARXIV13064705

[8] The Cauchy problem for semi-linear Klein-Gordon equations in de Sitter spacetime [J].

Nakamura, Makoto .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 410 (01) :445-454

[9]

Polya G., 1978, CLASSICS MATH, V193

[10] Future stability of the Einstein-non-linear scalar field system [J].

Ringstrom, Hans .

INVENTIONES MATHEMATICAE, 2008, 173 (01) :123-208

← 1 2 →