English

Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities

Analysis of PDEs 2015-05-13 v1

Abstract

The goal of this note is to state the optimal decay rate for solutions of the nonlinear fast diffusion equation and, in self-similar variables, the optimal convergence rates to Barenblatt self-similar profiles and their generalizations. It relies on the identification of the optimal constants in some related Hardy-Poincar\'e inequalities and concludes a long series of papers devoted to generalized entropies, functional inequalities and rates for nonlinear diffusion equations.

Keywords

Cite

@article{arxiv.0907.2986,
  title  = {Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities},
  author = {Matteo Bonforte and Jean Dolbeault and Gabriele Grillo and Juan-Luis Vázquez},
  journal= {arXiv preprint arXiv:0907.2986},
  year   = {2015}
}