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

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 "del v," i.e. the chemotactic term is given in the form -div(chi u vertical bar del v|(p-2) del v), for p is an element of(N/N-1,2), N > 2 for a positive constant chi when v satisfies the poisson equation -Delta v = u - 1/vertical bar Omega vertical bar integral(Omega)u(0)dx. We study the radially symmetric solutions under the assumption in the initial mass 1/vertical bar Omega vertical bar integral(Omega)u(0)dx > 6. For chi large enough, we present conditions in the initial data, such that any regular solution of the problem blows up at finite time.