  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.
