Global existence of a weak solution to unsaturated poroelasticity
Abstract
In this paper, we consider unsaturated poroelasticity, i.e., coupled hydro-mechanical processes in unsaturated porous media, modeled by a non-linear extension of Biot's quasi-static consolidation model. The coupled, elliptic-parabolic system of partial differential equations is a simplified version of the general model for multi-phase flow in deformable porous media obtained under similar assumptions as usually considered for Richards' equation. In this work, the existence of a weak solution is established using regularization techniques, the Galerkin method, and compactness arguments. The final result holds under non-degeneracy conditions and natural continuity properties for the non-linearities. The assumptions are demonstrated to be reasonable in view of geotechnical applications.
Keywords
Cite
@article{arxiv.1909.06679,
title = {Global existence of a weak solution to unsaturated poroelasticity},
author = {Jakub Wiktor Both and Iuliu Sorin Pop and Ivan Yotov},
journal= {arXiv preprint arXiv:1909.06679},
year = {2019}
}