  We consider a recent plate model obtained as a scaled limit of the three
dimensional Biot system of poro-elasticity. The result is a "2.5" dimensional
linear system that couples traditional Euler-Bernoulli plate dynamics to a
pressure equation in three dimensions, where diffusion acts only transversely.
We alow the permeability function to be time-dependent, making the problem
non-autonomous and disqualifying much of the standard abstract theory. Weak
solutions are defined in the so called quasi-static case, and the problem is
framed abstractly as an implicit, degenerate evolution problem. Utilizing the
theory for weak solutions to implicit evolution equations, we obtain existence
of solutions. Uniqueness is obtained under additional hypotheses on the
regularity of the permeability. We address the inertial case in an appendix, by
way of semigroup theory. The work here provides a baseline theory of weak
solutions for the poro-elastic plate, and exposits a variety of interesting
related models and associated analytical investigations.
