Weak solutions for a poro-elastic plate system

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