有限光滑的弹性wave equation
The elastic wave equation of limited smoothness
摘要：
我们建立了一个去耦结果的$P$和$S$波的线性，各向同性弹性，在设置的二次可微Lamé参数。准确地说，我们证明了波传播算子的$P\leftrightarrow S$组件是正则化的一阶$L^2$数据，通过建立对角化的弹性系统模一个$L^2$ -有界算子。在设置二次可微系数时实现对角化取决于具有特定结构的共轭算子的符号。
英文摘要：
We establish a decoupling result for the $P$ and $S$ waves of linear, isotropic elasticity, in the setting of twice-differentiable Lamé parameters. Precisely, we show that the $P\leftrightarrow S$ components of the wave propagation operator are regularizing of order one on $L^2$ data, by establishing the diagonalization of the elastic system modulo a $L^2$-bounded operator. Effecting the diagonalization in the setting of twice-differentiable coefficients depends upon the symbol of the conjugation operator having a particular structure.
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