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arXiv · 2011.12356

Nonlinear Quasi-static Poroelasticity

Lorena Bociu·Justin T. Webster
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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.

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Lorena Bociu, Justin T. Webster. 2020-11-24. Nonlinear Quasi-static Poroelasticity. https://arxiv.org/abs/2011.12356

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