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# M. E. Taylor Analysis and PDE Seminar – Ruoyu P.T. Wang (University College London)

## October 11, 2023 @ 3:30 pm - 4:30 pm

**Unbounded damped waves: backward uniqueness and polynomial stability**

**Abstract**. In this talk, we discuss the wave semigroup with an unbounded damping. In such a setting, there are explicit 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, Eulerâ€”Bernoulli beams, and Kelvinâ€”Voigt damping.