2021 journal article
Nonlinear quasi-static poroelasticity & nbsp;
Nonlinear quasi-static poroelasticity & nbsp; JOURNAL OF DIFFERENTIAL EQUATIONS, 296, 242–278.
author keywords: Poroelasticity; Nonlinear coupling; Implicit evolution; Fixed point methods
open access via arxiv.org (repository)
Source: Web Of Science
Added: July 19, 2021
We analyze a quasi-static Biot system of poroelasticity for both compressible and incompressible constituents. The main feature of this model is a nonlinear coupling of pressure and dilation through the system's permeability tensor. Such a model has been analyzed previously from the point of view of constructing weak solutions through a fully discretized approach. In this treatment, we consider simplified Dirichlet type boundary conditions in both the elastic displacement and pressure variables and give a full treatment of weak solutions. Our construction of weak solutions for the nonlinear problem is based on a priori estimates, a requisite feature in addressing the nonlinearity. We utilize a spatial semi-discretization and employ a multi-valued fixed point argument for a clear construction of weak solutions. We also provide regularity criteria for uniqueness of solutions.