论文标题
非线性弹性波的散射和刚度
Scattering and Rigidity for Nonlinear Elastic Waves
论文作者
论文摘要
对于库奇的非线性弹性波方程的问题，具有三维各维学，均质和高弹性材料满足无效状态的三维弹性波方程，在R. agemi（Invent。142（2000）225----250）和T. C. C. C. C. Sideris（Ann。Math。Math。151（2001）（2001（2001）（2001年）中，全球具有较小初始数据的经典解决方案的存在。在本文中，我们将考虑全球解决方案的渐近行为。我们首先表明，全局解决方案将散布，即，随着时间的时间，它会在能量意义上趋于无限。我们还证明了以下刚度结果：如果散射数据消失，则全局解决方案也将相同消失。系统的变分结构将在我们的论点中起关键作用。
For the Cauchy problem of nonlinear elastic wave equations of three dimensional isotropic, homogeneous and hyperelastic materials satisfying the null condition, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225--250) and T. C. Sideris (Ann. Math. 151(2000) 849--874), independently. In this paper, we will consider the asymptotic behavior of global solutions. We first show that the global solution will scatter, i.e., it will converge to some solution of linear elastic wave equations as time tends to infinity, in the energy sense. We also prove the following rigidity result: if the scattering data vanish, then the global solution will also vanish identically. The variational structure of the system will play a key role in our argument.
