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

Ansgar Jüngel | Zendy; Stefan Schuchnigg | Zendy

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

Author(s) -

Ansgar Jüngel,

Stefan Schuchnigg

Publication year - 2017

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2017241

Subject(s) - exponential function , entropy (arrow of time) , dimension (graph theory) , porous medium , exponential decay , mathematics , discrete space , exponential growth , nonlinear system , space (punctuation) , mathematical analysis , statistical physics , porosity , physics , thermodynamics , pure mathematics , computer science , quantum mechanics , materials science , composite material , operating system

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.

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