Global existence versus blow up for some models of interacting particles

Details Global existence versus blow up for some models of interacting particles Global existence versus blow up for some models of interacting particles

2006-03-28

arxiv.org/abs/math/0603656v1

Colloq. Math. 106, 2 (2006) 293--303

Mathematics

Analysis of PDEs

Colloq. Math. (to appear)

Scientific paper

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.

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