Global existence versus blow up for some models of interacting particles
Volume 106 / 2006
Colloquium Mathematicum 106 (2006), 293-303
MSC: 35K60, 35B40, 82C21.
DOI: 10.4064/cm106-2-9
Abstract
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 Debye–Hückel 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 due to S. Montgomery-Smith.
