Nonresonance and global existence of prestressed nonlinear elastic waves
  The nonlinear hyperbolic system of pde's governing the evolution of the deformation of isotropic hyperelastic materials is considered. In the absence of boundaries and with an additional nonresonance or null condition, the system has global smooth solutions starting close to a one-parameter family of homogeneous dilations. The proof combines energy estimates with new decay estimates for the linear problem. 
Thomas C. Sideris