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math.AP2023★ 1 cited
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…
math.AP2023
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…