Wasserstein geometry of porous medium equation
Copyright policy )Wasserstein geometry of porous medium equation
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.
\(q\)-Gaussian measure, functional inequality, Nonlinear parabolic equations, Geometric probability and stochastic geometry, Degenerate parabolic equations, Spaces of measures, Mathematical Physics, Analysis
\(q\)-Gaussian measure, functional inequality, Nonlinear parabolic equations, Geometric probability and stochastic geometry, Degenerate parabolic equations, Spaces of measures, Mathematical Physics, Analysis
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