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International Mathematics Research Notices (2007) Vol. 2007 : article ID rnm034, 43 pages, doi:10.1093/imrn/rnm034 published on June 18, 2007
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Copyright © The Author 2007. Published by Oxford University Press.

Elastic Waves in Exterior Domains Part II: Global Existence with a Null Structure

Jason Metcalfe1, and Becca Thomases2

1 Department of Mathematics, University of California, Berkeley, CA 94720-3840
2 Courant Institute of Mathematical Sciences, New York University, New York, NY 10012

Correspondence: Correspondence to be sent to: Jason Metcalfe, Department of Mathematics, University of California, Berkeley, CA 94720-3840. e-mail: metcalfe{at}math.berkeley.edu

In this paper, we prove that solutions to a problem in nonlinear elasticity corresponding to small initial displacements exist globally in the exterior of a nontrapping obstacle. The medium is assumed to be homogeneous, isotropic, and hyperelastic, and the nonlinearity is assumed to satisfy a null condition. The techniques contained herein would allow for more complicated geometries provided that there is a sufficient decay of local energy for the linearized problem.

Communicated by Sergiu Klainerman


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