Nonlinear quasi-static poroelasticity

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:296

Article

Bociu, Lorena¹  Webster, Justin T.² 

[1] North Carolina State Univ, 2311 Stinson Dr, Raleigh, NC 27607 USA

[2] Univ Maryland, 1000 Hilltop, Baltimore, MD 21250 USA

关键词: Poroelasticity;    Nonlinear coupling;    Implicit evolution;    Fixed point methods;   

DOI  :  10.1016/j.jde.2021.05.060

来源: Elsevier

【 摘 要 】

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. (c) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free