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

2006/05/04 by Jason Metcalfe, Metcalfe, Jason, Becca Thomases +1 · 1 citation
Mathematics · #35L70 #74B20 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35L70 #msc:74B20

paper · pdf · doi:10.48550/arxiv.math/0605110

arxiv created 2006/05/04 · arxiv updated 2009/12/01

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.

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• Long-Time Existence of Quasilinear Wave Equations Exterior to Star-shaped Obstacle in 2D

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