Degenerate Damping in Interacting Elastic Systems

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