Wasserstein geometry of porous medium equation |
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Authors: | Asuka Takatsu |
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Institution: | 1. Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan;2. Institut des Hautes Études Scientifiques, Bures-sur-Yvette 91440, France;3. Max-Planck-Intitut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany |
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Abstract: | We study the porous medium equation with emphasis on q-Gaussian measures, which are generalizations of Gaussian measures by using power-law distribution. On the space of q-Gaussian measures, the porous medium equation is reduced to an ordinary differential equation for covariance matrix. We introduce a set of inequalities among functionals which gauge the difference between pairs of probability measures and are useful in the analysis of the porous medium equation. We show that any q-Gaussian measure provides a nontrivial pair attaining equality in these inequalities. |
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Keywords: | 60D05 46E27 |
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