We consider nonlinear diffusive evolution equations posed on bounded spacedomains, governed by fractional Laplace-type operators, and involving porousmedium type nonlinearities. We establish existence and uniqueness results in asuitable class of solutions using the theory of maximal monotone operators ondual spaces. Then we describe the long-time asymptotics in terms ofseparate-variables solutions of the friendly giant type. As a by-product, weobtain an existence and uniqueness result for semilinear elliptic non localequations with sub-linear nonlinearities. The Appendix contains a review of thetheory of fractional Sobolev spaces and of the interpolation theory that areused in the rest of the paper.
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