From resolvent estimates to damped waves

摘要: In this paper, we show how to obtain decay estimates for the damped wave equation on a compact manifold without geometric control via knowledge of dynamics near undamped set. We that if replacing damping term with higher-order complex absorbing potential gives an operator enjoying polynomial resolvent bounds real axis, then “resolvent” associated our problem enjoys same order. It is known necessary can also be obtained gluing from corresponding non-compact models.