Sharp Decay Rate for the Damped Wave Equation With Convex-Shaped Damping
Sharp Decay Rate for the Damped Wave Equation With Convex-Shaped Damping
Abstract We revisit the damped wave equation on two-dimensional torus where the damped region does not satisfy the geometric control condition. It was shown in [1] that, for sufficiently regular damping, the damped wave equation is stale at a rate sufficiently close to $t^{-1}$. We show that if the damping …