Nonlinear quasi-static poroelasticity

We analyze a quasi-static Biot system of poroelasticity for both compressible and incompressible constituents. The main feature this model is nonlinear coupling pressure dilation through the system's permeability tensor. Such has been analyzed previously from point view constructing weak solutions fully discretized approach. In treatment, we consider simplified Dirichlet type boundary conditions in elastic displacement variables give full treatment solutions. Our construction problem based on priori estimates, requisite addressing nonlinearity. utilize spatial semi-discretization employ multi-valued fixed argument clear also provide regularity criteria uniqueness