Abstract
In this paper, we study the Wasserstein gradient flow structure of the porous medium equation restricted to q-Gaussians. The JKO-formulation of the porous medium equation gives a variational functional Kh, which is the sum of the (scaled-) Wasserstein distance and the internal energy, for a time step h. We prove that, for the case of q-Gaussians on the real line, Kh is asymptotically equivalent, in the sense of Γ-convergence as h tends to zero, to a rate-large-deviation-like functional. The result explains why the Wasserstein metric as well as the combination of it with the internal energy play an important role.
Original language | English |
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Pages (from-to) | 85-106 |
Number of pages | 22 |
Journal | Asymptotic Analysis |
Volume | 92 |
Issue number | 1-2 |
DOIs | |
Publication status | Published - 2015 |
Keywords
- porous medium equation
- Gamma-convergence
- Wasserstein gradient flow
- variational methods