Schulz R (2020)
Publication Type: Journal article
Publication year: 2020
Book Volume: 483
Article Number: 123613
Journal Issue: 2
DOI: 10.1016/j.jmaa.2019.123613
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.
APA:
Schulz, R. (2020). Degenerate equations for flow and transport in clogging porous media. Journal of Mathematical Analysis and Applications, 483(2). https://doi.org/10.1016/j.jmaa.2019.123613
MLA:
Schulz, Raphael. "Degenerate equations for flow and transport in clogging porous media." Journal of Mathematical Analysis and Applications 483.2 (2020).
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