Nonlinear Quasi-static Poroelasticity
Loading...
Author/Creator
Author/Creator ORCID
Date
2021-06-10
Type of Work
Department
Program
Citation of Original Publication
Bociu, Lorena, & Justin T.Webster. "Nonlinear quasi-static poroelasticity." Journal of Differential Equations 296 (25 September 2021): 242-278. https://doi.org/10.1016/j.jde.2021.05.060
Rights
This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
Subjects
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 the elastic displacement and pressure variables and give a full treatment of weak solutions. Our construction of weak solutions for the nonlinear problem is natural and based on a priori estimates, a requisite feature in addressing the nonlinearity. This is in contrast to previous work which exploits linearity or monotonicity in the permeability, both of which are not available here. We utilize a spatial semi-discretization and employ a multi-valued fixed point argument in for a clear construction of weak solutions. We also provide regularity criteria for uniqueness of solutions.