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

Global existence versus blow up for some models of interacting particles

Piotr Biler 1, Lorenzo Brandolese 2

(2006)

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.

1:	Instytut Matematyczny
	Uniwersytet Wroclawski
2:	Institut Camille Jordan (ICJ)
	CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon

Subject

:

Mathematics/Analysis of PDEs

Keyword(s): Keller-Segel model – chemotaxis – Debye system – space-time decay – explosion

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From: Lorenzo Brandolese <>

Submitted on: Tuesday, 28 March 2006 16:09:58

Updated on: Thursday, 17 March 2011 20:17:34