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.