Self-Similar Blowup Solutions to an Aggregation Equation in Rⁿ

We present numerical simulations of radially symmetric finite time blowup for the aggregation equation uₜ=∇·(u∇ K*u), where the kernel $K(x)=|x|$. The dynamics of the blowup exhibits self-similar behavior in which zero mass concentrates at the core at the blowup time. Computations are performed in Rⁿ for n between 2 and 10 using a method based on characteristics. In all cases studied, the self-similarity exhibits second-kind (anomalous) scaling.