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Elastic waves in exterior domains, Part II: Global existence with a null structure

Research paper by Jason Metcalfe, Becca Thomases

Indexed on: 03 May '06Published on: 03 May '06Published in: Mathematics - Analysis of PDEs



Abstract

In this article, 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.