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

Willem J. M. van Oosterhout

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arXiv · 2408.15151

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

Willem J. M. van Oosterhout

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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.

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Willem J. M. van Oosterhout. 2024-08-27. Linearization of finite-strain poro-visco-elasticity with degenerate mobility. https://arxiv.org/abs/2408.15151

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