Finite time blow-up of the solution for a nonlinear parabolic equation of drift-diffusion type

Abstract

We discuss the existence of the blow-up solution for some nonlinear parabolic system called attractive drift-diffusion equation in two space dimensions. We show that if the initial data satisfies a threshold condition, the corresponding solution blows up in a finite time. This is a system case for the blow-up result of the chemotactic equation proved by Nagai [28] and Nagai-Senba-Suzuki [30] and gravitational interaction of particles by Biler-Nadzieja [7], [8].