Concerning the Strauss conjecture and almost global existence for nonlinear Dirichlet-wave equations in 4-dimensions

被引：37

作者：

Du, Yi ^{[2
]}

Metcalfe, Jason ^{[3
]}

Sogge, Christopher D. ^{[1
]}

Zhou, Yi ^{[2
]}

机构：

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

[2] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[3] Univ N Carolina, Dept Math, Chapel Hill, NC USA

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2008年 / 33卷 / 08期

关键词：

lifespan; nonlinear wave equations;

D O I：

10.1080/03605300802239803

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show the obstacle version of the Strauss conjecture holds when the spatial dimension is equal to 4. We also show that an almost global existence theorem of Hormander for (4 + 1)-dimensional Minkowski space holds in the obstacle setting. We use weighed space-time variants of the energy inequality and a variant of the classical Hardy inequality.

引用

页码：1487 / 1506

页数：20

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