Finite-time blow-up in quasilinear parabolic-elliptic chemotaxis system with nonlinear signal production (Q2325911)

The author studies a parabolic-elliptic system of chemotaxis with nonlinear diffusion and and nonlinear production of chemoattractant in bounded smooth domains of \(\mathbb{R}^n\), \(n\ge 1\). Conditions on nonlinearities are given that lead either to global-in-time existence of bounded solutions or to finite time blow-up of solutions for some initial data.