WIAS Preprint No. 3123, (2024)
Linearization of finite-strain poro-visco-elasticity with degenerate mobility
Authors
- van Oosterhout, Willem
ORCID: 0009-0003-0956-7222
2020 Mathematics Subject Classification
- 35K55 35K65 35Q74 74A30
Keywords
- Poro-visco-elasticity, diffusion equation, Moser iteration, linearization
DOI
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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