Wave Propagation in Smart Materials: Linear Elasticity

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    Abstract

    In this paper we deal with the behavior of solutions to hyperbolicequations 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\Deltau=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.
    Original languageEnglish
    Book seriesMat Report
    Issue number23
    Publication statusPublished - 1999

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