Global existence of solutions to multiple speed systems of quasilinear wave equations in exterior domains

被引：29

作者：

Metcalfe, J ^{[1
]}

Nakamura, M

Sogge, CD

机构：

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

[2] Tohoku Univ, Grad Sch Informat Sci, Sendai, Miyagi 9808579, Japan

[3] Johns Hopkins Univ, Dept Math, Baltimore, MD 21218 USA

来源：

FORUM MATHEMATICUM | 2005年 / 17卷 / 01期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1515/form.2005.17.1.133

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we prove global existence for certain multispeed Dirichlet-wave equations with quadratic nonlinearities outside of obstacles. We assume the natural null condition for systems of quasilinear wave equations with multiple speeds. The null condition only puts restrictions on the self-interactions of each wave family. We use the method of commuting vector fields and weighted space-time L-2 estimates.

引用

页码：133 / 168

页数：36

共 50 条

[1] ALMOST GLOBAL EXISTENCE FOR 4-DIMENSIONAL QUASILINEAR WAVE EQUATIONS IN EXTERIOR DOMAINS
Helms, John
Metcalfe, Jason
[J]. DIFFERENTIAL AND INTEGRAL EQUATIONS, 2014, 27 (9-10) : 837 - 878
[2] Global existence for semilinear wave equations in exterior domains
Nakao, M
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 47 (04) : 2497 - 2506
[3] GLOBAL EXISTENCE OF THE SOLUTIONS OF NONLINEAR PARABOLIC EQUATIONS IN EXTERIOR DOMAINS
陈韻梅
[J]. Chinese Annals of Mathematics, 1986, (04) : 498 - 522
[4] GLOBAL EXISTENCE OF THE SOLUTIONS OF NONLINEAR PARABOLIC EQUATIONS IN EXTERIOR DOMAINS
CHEN, YM
[J]. CHINESE ANNALS OF MATHEMATICS SERIES B, 1986, 7 (04) : 498 - 522
[5] GLOBAL EXISTENCE OF THE SOLUTIONS TO NONLINEAR HYPERBOLIC EQUATIONS IN EXTERIOR DOMAINS
陈韻梅
高剑敏
[J]. Chinese Annals of Mathematics, 1990, (03) : 315 - 329
[6] On global smooth solutions to the initial-boundary value problem for quasilinear wave equations in exterior domains
Nakao, M
[J]. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 2003, 55 (03) : 765 - 795
[7] ALMOST GLOBAL EXISTENCE FOR 3-D QUASILINEAR WAVE EQUATIONS IN EXTERIOR DOMAINS WITH NEUMANN BOUNDARY CONDITIONS
Yuan, M. E. N. G.
[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2022, : 3721 - 3753
[8] Global existence of null-form wave equations in exterior domains
Metcalfe, Jason
Sogge, Christopher D.
[J]. MATHEMATISCHE ZEITSCHRIFT, 2007, 256 (03) : 521 - 549
[9] Global existence of null-form wave equations in exterior domains
Jason Metcalfe
Christopher D. Sogge
[J]. Mathematische Zeitschrift, 2007, 256 : 521 - 549
[10] GLOBAL EXISTENCE OF THE SOLUTIONS TO NONLINEAR HYPERBOLIC-EQUATIONS IN EXTERIOR DOMAINS
CHEN, YM
GAO, JM
[J]. CHINESE ANNALS OF MATHEMATICS SERIES B, 1990, 11 (03) : 315 - 329

← 1 2 3 4 5 →