arXiv:1702.03780 Abstract | arXiv Analytics

arXiv:1702.03780 [math.AP]Abstract References Reviews Resources

A discrete Bakry-Emery method and its application to the porous-medium equation

Published 2017-02-13Version 1

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.

Categories: math.AP, math.NA

Subjects: 65J08, 65M06, 65M12, 65Q10

Keywords: exponential decay, application, abstract discrete bakry-emery method, space step sizes, nonlinear summation-by-parts formula

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