Degenerate equations for flow and transport in clogging porous media

In this article, we consider fluid flow and transport in evolving porous media including vanishing porosity. We analyze the corresponding equations for a given porosity function, which describes the evolution of the underlying saturated porous medium, and are particularly interested in partially clo...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical analysis and applications 2020-03, Vol.483 (2), p.123613, Article 123613
Main Author: Schulz, Raphael
Format: Article
Language:English
Subjects:
Decay behavior
Degenerate PDEs
Evolving porous media
Muckenhoupt weights
Weak solutions
Weighted Sobolev spaces
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this article, we consider fluid flow and transport in evolving porous media including vanishing porosity. We analyze the corresponding equations for a given porosity function, which describes the evolution of the underlying saturated porous medium, and are particularly interested in partially clogged media. Thereby, the hydrodynamic parameters (permeability, diffusivity) are assumed to depend on the porosity and degeneracies arise in case of clogging. Introducing appropriate weighted function spaces and including the degenerate parameters as weights of Muckenhoupt class, we are able to handle the degeneracy and obtain analytical results. We solve the underlying equations via saddle-point theory or an adjusted Rothe method by applying the useful properties of such weighted function spaces. Moreover, we obtain nonnegativity and boundedness for the weak solution to the transport equation. Finally, we are interested in the decay behavior of this solution with respect to the porosity.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2019.123613