On global existence for nonlinear wave equations outside of convex obstacles

Markus Keel, Hart F. Smith, Christopher D. Sogge

Research output: Contribution to journalArticle

10 Scopus citations

Abstract

The authors prove global existence of small solutions to a semilinear wave equation outside of convex obstacles. This extends results of Christodoulou and Klainerman who handled the Minkowski space version. The proof is a compromise of the methods of Christodoulou and Klainerman. It relies on local estimates proved earlier by Smith and Sogge together with classical energy decay estimates for the wave equation of Morawetz, Lax and Phillips.

Original languageEnglish (US)
Pages (from-to)805-842
Number of pages38
JournalAmerican Journal of Mathematics
Volume122
Issue number4
DOIs
StatePublished - Aug 2000

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