The APDE seminar on Monday, 4/24, will be given by Perry Kleinhenz (MSU) in-person in Evans 732, and will also be broadcasted online via Zoom from 4:10pm to 5:00pm PST. To participate, please email Federico Pasqualotto (firstname.lastname@example.org) or Mengxuan Yang (email@example.com).
Title: Energy decay for the damped wave equation
Abstract: The damped wave equation describes the motion of a vibrating system exposed to a damping force. For the standard damped wave equation, exponential energy decay is equivalent to the Geometric Control Condition (GCC). The GCC requires every geodesic to meet the positive set of the damping coefficient in finite time. A natural generalization is to allow the damping coefficient to depend on time, as well as position. I will give an overview of the classical results and discuss how a time dependent generalization of the GCC implies exponential energy decay. I will also mention some results for unbounded damping when the GCC is not satisfied.