Some uniqueness and continuous dependence theorems for nonlinear elastodynamics in exterior domains

Abstract

AMS (MOS) Nos. 73C50, 73C15; 35B30, 35M05

Uniqueness and Höolder continuous dependence upon the initial data of the null solution to the initial boundary value problem of nonlinear hyperelasticity are proved for exterior domains subject to mild asymptotic behaviour on the displacement, velocity and stress components. The strain-energy is not required to be locally sign-definite although at sufficiently large spatial distances it must be non-negative. Other limitations imposed on the strain-energy become identically satisfied upon reduction to the linear theory.