15 citations · 18 across the 14 of their papers we have counts for
14 papers
Hypoellipticity on time-periodic space-times
Sandro Coriasco, Perry Kleinhenz, Jared Wunsch
We study the hypoellipticity of operators on a product type Lorentzian manifold where the time variable is periodic. In particular, we prove that hypoellipticity holds for such tim…
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…
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. We…
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 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…
Optimal backward uniqueness and polynomial stability of second order equations with unbounded damping
Perry Kleinhenz, Ruoyu P. T. Wang
For general second order evolution equations, we prove an optimal condition on the degree of unboundedness of the damping, that rules out finite-time extinction. We show that contr…
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…
Sharp polynomial decay for polynomially singular damping on the torus
Perry Kleinhenz, Ruoyu P. T. Wang
We study energy decay rates for the damped wave equation with unbounded damping, without the geometric control condition. Our main decay result is sharp polynomial energy decay for…
Energy decay for the time dependent damped wave equation
Perry Kleinhenz
Energy decay is established for the damped wave equation on compact Riemannian manifolds where the damping coefficient is allowed to depend on time. Using a time dependent observab…
Sharp exponential decay rates for anisotropically damped waves
Blake Keeler, Perry Kleinhenz
In this article, we study energy decay of the damped wave equation on compact Riemannian manifolds where the damping coefficient is anisotropic and modeled by a pseudodifferential…
Decay rates for the damped wave equation with finite regularity damping
Perry Kleinhenz
Decay rates for the energy of solutions of the damped wave equation on the torus are studied. In particular, damping invariant in one direction and equal to a sum of squares of non…
Sharp polynomial decay rates for the damped wave equation with Hölder-like damping
Kiril Datchev, Perry Kleinhenz
We study decay rates for the energy of solutions of the damped wave equation on the torus. We consider dampings invariant in one direction and bounded above and below by multiples…
Stabilization rates for the damped wave equation with Hölder-regular damping
Perry Kleinhenz
We study the decay rate of the energy of solutions to the damped wave equation in a setup where the geometric control condition is violated. We consider damping coefficients which…