Asymptotic equivalence of the discrete variational functional and a rate-large-deviation-like functional in the Wasserstein gradient flow of the porous medium equation

M.H. Duong

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Abstract

In this paper, we study the Wasserstein gradient flow structure of the porous medium equation. We prove that, for the case of q -Gaussians on the real line, the functional derived by the JKO-discretization scheme is asymptotically equivalent to a rate-large-deviation-like functional. The result explains why the Wasserstein metric as well as the combination of it with the Tsallis-entropy play an important role.
Original languageEnglish
Publishers.n.
Number of pages17
Publication statusPublished - 2013

Publication series

NamearXiv.org
Volume1307.5184 [math.AP]

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