Nonresonance and global existence of prestressed nonlinear elastic waves

Details Nonresonance and global existence of prestressed nonlinear elastic waves Nonresonance and global existence of prestressed nonlinear elastic waves

2000-05-10

arxiv.org/abs/math/0005103v2

Ann. of Math. (2) 151 (2000), no. 2, 849-874

Mathematics

Analysis of PDEs

26 pages, published version

Scientific paper

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.

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