Linearization of finite-strain poro-visco-elasticity with degenerate mobility

TL;DR

This paper studies a nonlinear finite-strain poro-visco-elasticity model with degenerate mobility, proving boundedness of concentration and convergence to linear solutions under small external loads.

Contribution

It introduces a rigorous analysis of the finite-strain model, establishing boundedness and linearization results that were not previously available.

Findings

Boundedness of concentration via Moser iteration.

Convergence of nonlinear solutions to linear solutions under small loads.

Existence of weak solutions for the nonlinear model.

Abstract

A quasistatic nonlinear model for finite-strain poro-visco-elasticity is considered in the Lagrangian frame using Kelvin-Voigt rheology. The model consists of a mechanical equation which is coupled to a diffusion equation with a degenerate mobility. Having shown existence of weak solutions in a previous work, the focus is first on showing boundedness of the concentration using Moser iteration. Afterwards, it is assumed that the external loading is small, and it is rigorously shown that solutions of the nonlinear, finite-strain system converge to solutions of the linear, small-strain system.