Blow up of solutions for a Parabolic-Elliptic chemotaxis system with gradient dependent chemotactic coefficient

Abstract

We consider a Parabolic-Elliptic system of PDE’s with a chemotactic term in a N-dimensional unit ball describing the behavior of the density of a biological species “u” and a chemical stimulus “v.” The system includes a nonlinear chemotactic coefficient depending of “” i.e. the chemotactic term is given in the form for a positive constant χ when v satisfies the poisson equation We study the radially symmetric solutions under the assumption in the initial mass For χ large enough, we present conditions in the initial data, such that any regular solution of the problem blows up at finite time.