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.
|Number of pages||17|
|Publication status||Published - 2013|