Ruoyu Wang University College London
Unbounded damped waves: backward uniqueness and polynomial stability
In this talk, we discuss the wave semigroup with an unbounded damping. In such a
setting, there are surprising examples where the linear damped waves would go
into finite-time extinction. We will then find an optimal condition explicitly
on the unboundedness to guarantee that the finite-time extinction cannot happen.
We will also develop powerful yet flexible control-theoretic tools to establish
novel polynomial stability and energy decay results for a variety of damped
wave-like systems, including the linearised gravity water waves, Euler–Bernoulli
beams, and Kelvin–Voigt damping.