Looking for critical nonlinearity in the one-dimensional quasilinear Smoluchowski-Poisson system

Tomasz Cieślak, Philippe Laurençot

It is known that classical solutions to the one-dimensional quasilinear Smoluchowski-Poisson system with nonlinear diffusion $a(u)=(1+u{)}^{-p}$ may blow up in finite time if $p>1$ a…