Asymptotic behavior for nonlinear diffusion equations.

We describe the long time asymptotics of nonlinear diffusion equations by
two approaches: mass transportation techniques and entropy dissipation
methods. They allow to prove exponential convergence of certain entropy
functionals and the Wasserstein distance between probability measures.
This class of equations contains as particular cases: heat equation, the
porous medium-fast diffusion equation and nonlinear friction equations
introduced in the study of granular media.