Abstract damped wave equations: The optimal decay rate

Filippo Dell'Oro, Lorenzo Liverani, Vittorino Pata

The exponential decay rate of the semigroup $S(t)=e^{t\mathbb{A}}$ generated by the abstract damped wave equation $$\ddot{u}+2f(A)\dot{u}+Au=0$$ is here addressed, where $A$ is…