On the existence of radially symmetric blow-up solutions for the Keller-Segel model

We investigate the existence of radially symmetric solutions of the Keller-Segal model A(t) = del . (delA - AdelC), x is an element of Omega, t > 0 C-t = k(c)DeltaC - gammaC + alphachi(A - 1), x is an element of Omega, t > 0 partial derivativeA/partial derivativen = partial derivativeC/partial derivativen = 0, x is an element of partial derivativeOmega, t > 0 A(0, x) = A(0)(x) > 0, C(0, x) = C-0(x), x is an element of Omega, which blow up in finite or infinite time, i.e. lim(t --> Tmax) sup parallel toA(t, .)parallel to(Linfinity(Omega)) = infinity or lim(t --> Tmax) sup parallel toC(+)(t, .)parallel to(Linfinity(Omega)) = infinity for T-max less than or equal to infinity, under a larger class of initial data than in [10] and [11].