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.
Acknowledgment
The author wants to thank to the anonymous reviewers and also to professor Michael Winkler, for their helpful comments and suggestions.