Uniqueness of weak solutions to a high dimensional Keller–Segel equation with degenerate diffusion and nonlocal aggregation

This paper considers weak solutions to the degenerate Keller–Segel equation with nonlocal aggregation: ut=Δum−∇⋅(uB(u))ut=Δum−∇⋅(uB(u)) in Rd×R+Rd×R+, where B(u)=∇((−Δ)−β2u), d≥3d≥3, β∈[2,d)β∈[2,d), 1