Nonlinear quasi-static poroelasticity

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 vi...

Full description

Saved in:
Bibliographic Details
Published in:Journal of Differential Equations 2021-09, Vol.296, p.242-278
Main Authors: Bociu, Lorena, Webster, Justin T.
Format: Article
Language:English
Subjects:
Fixed point methods
Implicit evolution
Nonlinear coupling
Poroelasticity
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2021.05.060