# Diffusion in Poro-Elastic Media

@article{Showalter2000DiffusionIP, title={Diffusion in Poro-Elastic Media}, author={R. E. Showalter}, journal={Journal of Mathematical Analysis and Applications}, year={2000}, volume={251}, pages={310-340} }

Existence, uniqueness, and regularity theory is developed for a general initial-boundary-value problem for a system of partial differential equations which describes the Biot consolidation model in poro-elasticity as well as a coupled quasi-static problem in thermoelasticity. Additional effects of secondary consolidation and pore fluid exposure on the boundary are included. This quasi-static system is resolved as an application of the theory of linear degenerate evolution equations in Hilbert…

## 252 Citations

### Diffusion in deformable media

- Mathematics
- 2002

We begin with the initial-boundary-value problem for a coupled system of partial differential equations which describes the Biot consolidation model in poroelasticity. Existence, uniqueness and…

### DIFFUSION IN DEFORMABLE

- Mathematics

We begin with the initial-boundary-value problem for a coupled system of partial diierential equations which describes the Biot consolidation model in poro-elasticity. Existence, uniqueness and…

### Diffusion in poro‐plastic media

- Mathematics
- 2004

A model is developed for the flow of a slightly compressible fluid through a saturated inelastic porous medium. The initial‐boundary‐value problem is a system that consists of the diffusion equation…

### Finite Difference Schemes for Poro-elastic ProblemS

- Mathematics
- 2002

Abstract In this paper, we present a finite difference analysis of the consolidation problem for saturated porous media. In the classical model, the behaviour of the porous environment – fluid system…

### Mathematical Analysis of Diffusion Models in Poro-Elastic Media

- Mathematics
- 2003

We consider a coupled system of mixed hyperbolic-parabolic type which describes the Biot consolidation model in poro-elasticity as well as a coupled quasi-static problem in thermoelasticity. The…

### Advection-diffusion-reaction in poroelastic media. Part I: Well-posedness and discrete analysis

- MathematicsArXiv
- 2019

A PDE system modelling poromechanical processes interacting with diffusing and reacting solutes in the medium is analysed and the well-posedness of the nonlinear set of equations is investigated using fixed-point theory, Fredholm's alternative, a priori estimates, and compactness arguments.

### Di usion in poro-plastic media

- Mathematics
- 2004

A model is developed for the ow of a slightly compressible uid through a saturated inelastic porous medium. The initial-boundary-value problem is a system that consists of the di usion equation for…

### On existence-uniqueness of the solution in a nonlinear Biot's model

- Mathematics
- 2013

The response of elastic porous media under applied loads consists of an instantaneous deformation followed by a time dependent consolidation process associated with the drainage of the pore fluid. In…

### Well-posedness and discrete analysis for advection-diffusion-reaction in poroelastic media

- MathematicsApplicable Analysis
- 2021

A PDE system modelling poromechanical processes interacting with diffusing and reacting solutes in the medium is analysed and the well-posedness of the nonlinear set of equations is investigated using fixed-point theory, Fredholm's alternative, a priori estimates, and compactness arguments.

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