Remarks on Nonlinear Elastic Waves in the Radial Symmetry in 2-D
Analysis of PDEs
2015-12-25 v2
Abstract
In this manuscript we first give the explicit variational structure of the nonlinear elastic waves for isotropic, homogeneous, hyperelastic materials in 2-D. Based on this variational structure, we suggest a null condition which is a kind of structural condition on the nonlinearity in order to stop the formation of finite time singularities of local smooth solutions. In the radial symmetric case, inspired by Alinhac's work [3] on 2-D quasilinear wave equations, we show that such null condition can ensure the globalexistence of smooth solutions with small initial data.
Keywords
Cite
@article{arxiv.1512.01373,
title = {Remarks on Nonlinear Elastic Waves in the Radial Symmetry in 2-D},
author = {Dongbing Zha},
journal= {arXiv preprint arXiv:1512.01373},
year = {2015}
}