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math.AP2025
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…
math.AP2025
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…
math.AP2025
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…