%0 Journal Article
%T Global existence versus blow up for some models of interacting particles
%A Piotr Biler
%A Lorenzo Brandolese
%J Mathematics
%D 2006
%I arXiv
%X We study the global existence and space-time asymptotics of solutions for a class of nonlocal parabolic semilinear equations. Our models include the Nernst-Planck and the Debye-Hukel drift-diffusion systems as well as parabolic-elliptic systems of chemotaxis. In the case of a model of self-gravitating particles, we also give a result on the finite time blow up of solutions with localized and oscillating complex-valued initial data, using a method by S. Montgomery-Smith.
%U http://arxiv.org/abs/math/0603656v1