Elastic Waves in Exterior Domains Part II: Global Existence with a Null Structure
نویسنده
چکیده
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.
منابع مشابه
ar X iv : m at h / 06 11 48 9 v 1 [ m at h . A P ] 1 6 N ov 2 00 6 GLOBAL EXISTENCE OF NULL - FORM WAVE EQUATIONS IN EXTERIOR DOMAINS
Abstract. We provide a proof of global existence of solutions to quasilinear wave equations satisfying the null condition in certain exterior domains. In particular, our proof does not require estimation of the fundamental solution for the free wave equation. We instead rely upon a class of Keel-Smith-Sogge estimates for the perturbed wave equation. Using this, a notable simplification is made ...
متن کاملGlobal Existence of Solutions to Multiple Speed Systems of Quasilinear Wave Equations in Exterior Domains
1. Introduction. The goal of this paper is to prove global existence of solutions to quadratic quasilinear Dirichlet-wave equations exterior to a class of compact obstacles. As in Metcalfe-Sogge [22], the main condition that we require for our class of obstacles is exponential local energy decay (with a possible loss of regularity). Our result improves upon the earlier one of Metcalfe-Sogge [22...
متن کاملEffect of Micropolarity on the Propagation of Shear Waves in a Piezoelectric Layered Structure
This paper studies the propagation of shear waves in a composite structure consisting of a piezoelectric layer perfectly bonded over a micropolar elastic half space. The general dispersion equations for the existence of shear waves are obtained analytically in the closed form. Some particular cases have been discussed and in one special case the relation obtained is in agreement with existing r...
متن کاملAn Application of Kubota-yokoyama Estimates to Quasilinear Wave Equations with Cubic Terms in Exterior Domains
Small global solutions for quasilinear wave equations are considered in three space dimensions in exterior domains. The obstacles are compact with smooth boundary and the local energy near the obstacles is assumed to decay exponentially with a possible loss of regularity. The null condition is needed to show global solutions for quadratic nonlinearities.
متن کاملNonresonance and Global Existence of Prestressed Nonlinear Elastic Waves
This article considers the existence of global classical solutions to the Cauchy problem in nonlinear elastodynamics. The unbounded elastic medium is assumed to be homogeneous, isotropic, and hyperelastic. As in the theory of 3D nonlinear wave equations in three space dimensions, global existence hinges on two basic assumptions. First, the initial deformation must be a small displacement from e...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006