A critical blow-up exponent in a chemotaxis system with nonlinear signal production. (5th April 2018) - Winkler, Michael
Abstract: This paper is concerned with radially symmetric solutions of the Keller–Segel system with nonlinear signal production, as given by in the ball for and R > 0, where f is a suitably regular function generalizing the prototype determined by the choice, , with . The main results assert that if in this setting the number κ satisfies then for any prescribed mass level m > 0, there exist initial data u 0 with, for which the solution of the corresponding Neumann initial-boundary value problem blows up in finite time. The condition in ( ) is essentially optimal and is indicated by a complementary result according to which in the case, for widely arbitrary initial data, a global bounded classical solution can always be found.