Taylor and Francis Group, Applicable Analysis, 9(96), p. 1547-1560, 2017
DOI: 10.1080/00036811.2017.1286647
Full text: Download
This paper collects results concerning global rates and large time asymptotics of a fractional fast diffusion on the Euclidean space, which is deeply related with a family of fractional Gagliardo-Nirenberg-Sobolev inequalities. Generically, self-similar solutions are not optimal for the Gagliardo-Nirenberg-Sobolev inequalities, in strong contrast with usual standard fast diffusion equations based on non-fractional operators. Various aspects of the stability of the self-similar solutions and of the entropy methods like carr{é} du champ and R{é}nyi entropy powers methods are investigated and raise a number of open problems.