Almost collapse mass quantization in 2D Smoluchowski–Poisson equation

Abstract

We study Smoluchowski–Poisson equation in two space dimensions provided with Dirichlet boundary condition for the Poisson part. For this equation, several profiles of blowup solution have been noticed: blowup threshold on L1 norm of the initial value, finiteness of blowup points, formation of delta singularities called collapses, occurrence of type II blowup, exclusion of the boundary blowup point, and so forth. Here, we show the collapse mass quantization with possible residual terms. Copyright © 2015 John Wiley & Sons, Ltd.