Origin of the p-Laplacian and A. Missbach
Date
2018-01-13
Authors
Benedikt, Jiri
Girg, Petr
Kotrla, Lukas
Takac, Peter
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We describe the historical process of derivation of the p-Laplace operator from a nonlinear Darcy law and the continuity equation. The story begins with nonlinear flows in channels and ditches. As the nonlinear Darcy law we use the power law discovered by Smreker and verified in experiments by Missbach for flows through porous media in one space dimension. These results were generalized by Christianovitch and Leibenson to porous media in higher space dimensions. We provide a brief description of Missbach's experiments.
Description
Keywords
Porous medium, Filtration, Nonlinear Darcy law, Pressure-to-velocity power law, p-Laplacian
Citation
Benedikt, J., Girg, P., Kotrla, L., & Takac, P. (2018). Origin of the p-Laplacian and A. Missbach. <i>Electronic Journal of Differential Equations, 2018</i>(16), pp. 1-17.