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Published August 2000 | Submitted
Journal Article Open

On global existence for nonlinear wave equations outside of convex obstacles

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.

Additional Information

© 2000 Johns Hopkins University Press. Manuscript received July 28, 1999. Research supported in part by the NSF.

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August 19, 2023
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