  This paper proves the asymptotic stability of the multidimensional wave
equation posed on a bounded open Lipschitz set, coupled with various classes of
positive-real impedance boundary conditions, chosen for their physical
relevance: time-delayed, standard diffusive (which includes the
Riemann-Liouville fractional integral) and extended diffusive (which includes
the Caputo fractional derivative). The method of proof consists in formulating
an abstract Cauchy problem on an extended state space using a dissipative
realization of the impedance operator, be it finite or infinite-dimensional.
The asymptotic stability of the corresponding strongly continuous semigroup is
then obtained by verifying the sufficient spectral conditions derived by Arendt
and Batty (Trans. Amer. Math. Soc., 306 (1988)) as well as Lyubich and V\~u
(Studia Math., 88 (1988)).
