We study well-posedness and long-time behaviour of aggregation-diffusion
equations of the form ∂t∂ρ=Δρm+∇⋅(ρ(∇V+∇W∗ρ)) in the fast-diffusion
range, 0<m<1, and V and W regular enough. We develop a well-posedness
theory, first in the ball and then in Rd, and characterise the
long-time asymptotics in the space W−1,1 for radial initial data. In the
radial setting and for the mass equation, viscosity solutions are used to prove
partial mass concentration asymptotically as t→∞, i.e. the limit as
t→∞ is of the form αδ0+ρdx with
α≥0 and ρ∈L1. Finally, we give instances of W=0 showing that partial mass concentration does happen in infinite time,
i.e. α>0