%0 Journal Article
%T Finite-time blowup in a supercritical quasilinear parabolic-parabolic Keller-Segel system in dimension 2
%A Tomasz Cie£żlak
%A Christian Stinner
%J Mathematics
%D 2012
%I arXiv
%R 10.1007/s10440-013-9832-5
%X In this paper we prove finite-time blowup of radially symmetric solutions to the quasilinear parabolic-parabolic two-dimensional Keller-Segel system for any positive mass. This is done in case of nonlinear diffusion and also in the case of nonlinear cross-diffusion provided the nonlinear chemosensitivity term is assumed not to decay. Moreover, it is shown that the above-mentioned lack of non-decay assumption is essential with respect to keeping the dichotomy finite-time blowup against boundedness of solutions. Namely, we prove that without the non-decay assumption possible asymptotic behaviour of solutions includes also infinite-time blowup.
%U http://arxiv.org/abs/1201.3270v1