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arXiv:math/0603656 [math.AP]AbstractReferencesReviewsResources

Global existence versus blow up for some models of interacting particles

Piotr Biler, Lorenzo Brandolese

Published 2006-03-28Version 1

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.

Comments: Colloq. Math. (to appear)
Journal: Colloq. Math. 106, 2 (2006) 293--303
Categories: math.AP
Subjects: 35K55, 92C17, 35Q60
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