Electron. J. Differential Equations,
Vol. 2018 (2018), No. 16, pp. 1-17.
Origin of the p-Laplacian and A. Missbach
Jiri Benedikt, Petr Girg, Lukas Kotrla, Peter Takac
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.
Submitted October 22, 2017. Published January 13, 2018.
Math Subject Classifications: 76S05, 35Q35.
Key Words: Porous medium; filtration; nonlinear Darcy law;
pressure-to-velocity power law; p-Laplacian.
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Jiri Benedikt
Department of Mathematics and NTIS
Faculty of Applied Scences, University of West Bohemia
Univerzitni 8, CZ-306\,14 Plzen, Czech Republic
email: benedikt@kma.zcu.cz
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Petr Girg
Department of Mathematics and NTIS
Faculty of Applied Scences, University of West Bohemia
Univerzitni 8, CZ-306 14~Plzen, Czech Republic
email: pgirg@kma.zcu.cz
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Lukas Kotrla
Department of Mathematics and NTIS
Faculty of Applied Scences, University of West Bohemia
Univerzitni 8, CZ-306 14 Plzen, Czech Republic
email: kotrla@ntis.zcu.cz
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Peter Takac
Institut fur Mathematik, Universitat Rostock
Germany
email: peter.takac@uni-rostock.de
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