Stabilization of the elastodynamic equations with a degenerate locally distributed dissipation

We consider the dynamic elasticity equations with a locally distributed damping in a bounded domain. The local dissipation of the form a(x)yt involves coefficients a that vanish on a negligible portion of the subset where the damping is effective. Using multiplier techniques, interpolation inequalities, and a judicious application of Hölder inequality, we prove sharp energy decay estimates. The results obtained generalize and improve on earlier works by Nakao, and the author in the framework of the ordinary wave equation.