Some existence-uniqueness results for a class of one-dimensional nonlinear Biot models

DOI10.1016/j.na.2004.10.023zbMath1068.35003OpenAlexW2137363668MaRDI QIDQ1776911

Patrick Saint-Macary, Hélène Barucq, Monique Madaune-Tort

Publication date: 12 May 2005

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2004.10.023

zbMATH Keywords

existenceuniquenesshyperbolic-parabolic systemquasi-static caseGalerkin approximantsporo-elastic media

Mathematics Subject Classification ID

Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10)

Related Items

A Galerkin Method for Biot Consolidation Model, Stabilized Lowest-Order Finite Element Approximation for Linear Three-Field Poroelasticity, The role of structural viscoelasticity in deformable porous media with incompressible constituents: applications in biomechanics, On the role of poroelasticity for modeling of stress fields in geothermal reservoirs, A local and global well-posedness results for the general stress-assisted diffusion systems, Numerical methods for a one-dimensional non-linear Biot's model, A weak solution of a stochastic nonlinear problem

Cites Work

• Perturbations singulières dans les problèmes aux limites et en contrôle optimal
• Diffusion in poro-elastic media
• A finite difference analysis of Biot's consolidation model
• On the existence and the asymptotic stability of solutions to the equations of linear thermoelasticity
• Diffusion in poro-plastic media
• Theory of Elasticity and Consolidation for a Porous Anisotropic Solid
• Single‐phase flow in composite poroelastic media
• Explicit diffusive kinetic schemes for nonlinear degenerate parabolic systems
• Asymptotic Behavior of Semidiscrete Finite-Element Approximations of Biot’s Consolidation Problem
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