Nonlinear Quasi-static Poroelasticity
Abstract
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.
Keywords
Cite
@article{arxiv.2011.12356,
title = {Nonlinear Quasi-static Poroelasticity},
author = {Lorena Bociu and Justin T. Webster},
journal= {arXiv preprint arXiv:2011.12356},
year = {2021}
}