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arXiv · 1512.01373

Remarks on Nonlinear Elastic Waves in the Radial Symmetry in 2-D

Dongbing Zha
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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.

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Dongbing Zha. 2015-12-24. Remarks on Nonlinear Elastic Waves in the Radial Symmetry in 2-D. https://arxiv.org/abs/1512.01373

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