%0 Journal Article
%T Existence, Uniqueness and Asymptotic behaviour for fractional porous medium equations on bounded domains
%A Matteo Bonforte
%A Yannick Sire
%A Juan Luis Vazquez
%J Mathematics
%D 2014
%I arXiv
%X We consider nonlinear diffusive evolution equations posed on bounded space domains, governed by fractional Laplace-type operators, and involving porous medium type nonlinearities. We establish existence and uniqueness results in a suitable class of solutions using the theory of maximal monotone operators on dual spaces. Then we describe the long-time asymptotics in terms of separate-variables solutions of the friendly giant type. As a by-product, we obtain an existence and uniqueness result for semilinear elliptic non local equations with sub-linear nonlinearities. The Appendix contains a review of the theory of fractional Sobolev spaces and of the interpolation theory that are used in the rest of the paper.
%U http://arxiv.org/abs/1404.6195v3