Ates of the rate of stabilization of solutions of exterior mixed problems for a class of evolution systems

A study is made of the behavior for large time of solutions of the exterior mixed problem for the evolution system
$$ u_{tt}+A(x,D_x)u=0, $$
where $A(x,D_x)$ is a strongly elliptic operator of order $2l$ ($ l\geqslant1$). Sharp estimates are obtained for certain weighted norms of the solutions as $t\to\infty$.