6 papers
Optimal decay for waves damped by superellipses
B. Achammer, Perry Kleinhenz
Energy decay rates for solutions of the damped wave equation on the torus are known to be influenced by the geometry of the damped set and the growth properties of the damping. In…
Sharp energy decay rates for the damped wave equation on the torus via non-polynomial derivative bound conditions
Perry Kleinhenz
For the damped wave equation on the torus, when some geodesics never meet the positive set of the damping, energy decay rates are known to depend on derivative bounds and growth pr…
Observability of Schrödinger equations in Euclidean space
Walton Green, Perry Kleinhenz
In this paper we introduce a new dynamical condition, the comb geometric control condition, which is sufficient for observability of the Schrödinger equation in Euclidean space. W…
Integrated Local Energy Decay for Waves with Time-Dependent Damping
Perry Kleinhenz, Michael McNulty
We prove integrated local energy decay for solutions of the damped wave equation with time-dependent damping satisfying an appropriate generalization of the geometric control condi…
Geometry of wave damping on the torus
Kiril Datchev, Perry Kleinhenz, Antoine Prouff
Energy decay rates of damped waves on the torus depend on the behavior of the damping near the undamped region and on the geometry of the damped set. In this paper we refine these…
Sharp conditions for exponential and non-exponential uniform stabilization of the time-dependent damped wave equation
Perry Kleinhenz
It is classical that uniform stabilization of solutions to the autonomous damped wave equation is equivalent to every geodesic meeting the positive set of the damping, which is cal…