The HADES seminar on Tuesday, October 20th will be given by Ruoyu Wang via Zoom from 3:40 to 5 pm.

Speaker: Ruoyu Wang (Northwestern)

Abstract: Lebeau (’93) suggested that on a compact manifold the damped waves decay logarithmically with merely some smooth damping inside a small open set. This phenomenon exploits the Carleman estimate establishing the exponentially weak observability. The natural generalisation of “small” sets to establish such exponential weak observability on noncompact manifolds is the Network Control Condition, formulated by Burq and Joly (’16), an condition requiring an upper bound of distance from the region of observability to any points on the manifold. We will show that this condition guarantees the exponentially weak observability on cylinders and scattering (asymptotically conic) manifolds, and henceforth derive a logarithmic decay for the damped waves in the high frequency regime, via a n-weight Carleman argument.