Asymptotic behaviour of thin poroelastic layers

We consider the deformation behaviour of thin poroelastic layers where the governing equations include a non-constant permeability. We consider both t he small and long time scale limits and by using appropriate perturbation s eries reduce the poroelastic equations to one-dimensional diffusion equatio ns. We particularly consider the cases of an indented porous layer, a layer relaxing after an initial disturbance and a layer with embedded sources. B oth axisymmetric and two-dimensional geometries are considered.