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On global existence for nonlinear wave equations outside of convex obstacles

Keel, Markus Aloysius and Smith, Hart F. and Sogge, Christopher Donald (2000) On global existence for nonlinear wave equations outside of convex obstacles. American Journal of Mathematics, 122 (4). pp. 805-842. ISSN 0002-9327. http://resolver.caltech.edu/CaltechAUTHORS:20170408-155512840

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1353/ajm.2000.0029DOIArticle
https://arxiv.org/abs/math/9912201arXivDiscussion Paper
http://www.jstor.org/stable/25099015JSTORArticle
Additional Information:© 2000 Johns Hopkins University Press. Manuscript received July 28, 1999. Research supported in part by the NSF.
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Record Number:CaltechAUTHORS:20170408-155512840
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170408-155512840
Official Citation:Keel, Markus, Hart F. Smith, and Christopher D. Sogge. "On Global Existence for Nonlinear Wave Equations outside of Convex Obstacles." American Journal of Mathematics 122, no. 4 (2000): 805-42. http://www.jstor.org/stable/25099015.
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ID Code:76090
Collection:CaltechAUTHORS
Deposited By: 1Science Import
Deposited On:30 May 2017 20:59
Last Modified:30 May 2017 20:59

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