2021/2023 UNC Greensboro PDE Conference.
Electron. J. Diff. Eqns., Conference 26 (2022), pp. 179-200.

Title: p-Laplacian in phenomenological modeling of flow in porous media and CFD simulations

Authors: Petr Girg (Univ. of West Bohemia, Czech Republic)
         Lukas Kotrla  (Univ. of West Bohemia, Czech Republic)
         Anezka Svandova (Univ. of West Bohemia, Czech Republic)
 
Abstract: 
The aim of this article is to discuss several aspects of connections between the
p-Laplacian and mathematical models in hydrology. 
At first we present models of groundwater flow in phreatic aquifers and models of irrigation and drainage that lead to quasilinear parabolic equations involving the p-Laplacian. 
Next, we survey conditions of validity of Strong Maximum Principle and Strong Comparison Principle for this type of problems. Finally, we employ computer fluid dynamics simulations to realistic scenario of fracture networks to estimate values of the parameters
of constitutive laws governing groundwater flow in the context of fractured
hard-rock aquifers.   

Published May 13, 2025.
Math Subject Classifications: 76S05, 35Q35, 35K92.
Key Words: p-Laplacian; porous medium; filtration; Darcy's law;  pressure-to-velocity power law.