Wave Propagation in Smart Materials: Wave Propagation in Smart Materials Linear Elasticity

In this paper we deal with the behavior of solutions to hyperbolic equations such as the wave equation: \begin{equation}\label{waveeq1} \frac{\partial^2}{\partial t^2}u-\Delta u=f, \end{equation} or the equations of linear elasticity for an isotropic medium: \begin{equation}\label{elasteq1} \frac{\partial^2}{\partial t^2}u -(\lambda+\mu){\text{\rm grad div}} u -\mu\Delta u=0, \end{equation} where $u=u(t,x)$ denotes a 3-vector field on $\Bbb R\times\Bbb R^3$, and $\lambda$ and $\mu$ are the Lame-constants.