  We investigate and clarify the mathematical properties of linear poro-elastic
systems in the presence of classical (linear, Kelvin-Voigt) visco-elasticity.
In particular, we quantify the time-regularizing and dissipative effects of
visco-elasticity in the context of the quasi-static Biot equations. The full,
coupled pressure-displacement presentation of the system is utilized, as well
as the framework of implicit, degenerate evolution equations, to demonstrate
such effects and characterize linear poro-visco-elastic systems. We consider a
simple presentation of the dynamics (with convenient boundary conditions, etc.)
for clarity in exposition across several relevant parameter ranges. Clear
well-posedness results are provided, with associated a priori estimates on the
solutions. In addition, precise statements of admissible initial conditions in
each scenario are given.
