Long-time asymptotic expansions for nonlinear diffusions in Euclidean space
Jochen Denzler, Herbert Koch, Robert J. McCann · Contemporary mathematics - American Mathematical Society · 2016
We give a brief introduction to some recent developments concerning the long-time asymptotics of the porous medium and fast diffusion equations, focusing in particular on results contained in a recent monograph by the authors which rigorously relate the higher asymptotics of the nonlinear dynamics to its linearized spectrum for the latter equation. The statements and techniques are motivated using a comparison to the more familiar situation of the evolution towards Gaussian produced by the standard heat flow.