Sharp Polynomial Decay for Waves Damped from the Boundary in Cylindrical Waveguides

We study the decay of global energy for the wave equation with H\"older continuous damping placed on the C^{1,1}-boundary of compact and non-compact waveguides with star-shaped cross-sections. We show there is sharp t^{-1/2}-decay when the damping is uniformly bounded from below on the cylindrical wall of product cylinders where the... Show more