Singular damped waves on manifolds
Ruoyu Wang (UCL)
We will discuss a damped wave semigroup for damping exhibiting Hölder-type blowup near a hypersurface on a compact manifold. We will use vector field methods to prove a sharp energy decay result for singular damping on the torus, where the optimal rate of energy decay explicitly depends on the singularity of the damping. Dynamically, such fine rates result from that the transverse propagation of lower-order regularity fails to penetrate through the hypersurface where the damping potential is singular. This is a joint work with Perry Kleinhenz.
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