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A. Jüngel, S. Schuchnigg:
"A discrete Bakry-Emery method and its application to the porous-medium equation";
in: "ASC Report 05/2017", herausgegeben von: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2017, ISBN: 978-3-902627-10-0, S. 1 - 22.

The exponential decay of the relative entropy associated to a fully discrete porous-medium equation in one space dimension is shown by means of a discrete Bakry-Emery approach. The first ingredient of the proof is an abstract discrete Bakry-Emery method, which states conditions on a sequence under which the exponential decay of the discrete entropy follows. The second ingredient is a new nonlinear summation-by-parts formula which is inspired by systematic integration by parts developed by Matthes and the first author. Numerical simulations illustrate the exponential decay of the entropy for various time and space step sizes.

Finite differences, Bakry-Emery method, large-time asymptotics, systematic integration by parts

http://www.asc.tuwien.ac.at/preprint/2017/asc05x2017.pdf