Kaïs Ammari, “Semigroup Regularity and Decay for Elastic Systems with Degenerate Coupling Damping”

We study the regularity and stability of coupled elastic systems subject to two distinct damping mechanisms: one acting through the average velocity, and the other through a fractional power of the elastic operator. The resulting damping matrix is degenerate, meaning that dissipation does not act equally on all components of the system. Using a frequency-domain approach based on resolvent estimates, we describe how this degeneracy affects the regularity of the associated semigroup and the decay rate of solutions. The results obtained are shown to be optimal, and are relevant to applications in structural mechanics and vibration control.