Self-similar Dynamics in the Critical $p$-Laplacian Patlak-Keller-Segel Model: Shrinking Blow-up and Expanding Propagation

Chunhua Jin, Fengqing Zhang

In this paper, we study the following Patlak-Keller-Segel model with $p$-Laplacian diffusion \begin{align*} \left\{ \begin{aligned} &ρ_t=\nabla \cdot \left( \left| \nabla ρ\right|^…