Derivation of non-polynomial fractional diffusions from the generalized exclusion with a slow barrier

Abstract: In this article we derive in the hydrodynamic limit a generalized fractional porous medium equation, in the sense that the regional fractional Laplacian is applied to a function of the density given in terms of a power series, instead of a polynomial. The hydrodynamic limit is obtained considering a microscopic dynamics of random particles with long range interactions, but the jump rate highly depends on the occupancy near the sites where the interactions take place. This system is also studied in the presence of a "slow barrier" that hinders the flow of mass between two half-spaces.