An integro-differential equation arising as a limit of individual cell-based models

In this paper, we study mathematical properties of an integro-differential equation that arises as a particular limit case in the study of individual cell-based model. We obtain global well-posedness for some classes of interaction potentials and finite time blow-up for others. The existence of spac...

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Bibliographic Details
Published in:Journal of Differential Equations 2006-03, Vol.222 (2), p.341-380
Main Authors: Bodnar, M., Velazquez, J.J.L.
Format: Article
Language:English
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Summary:In this paper, we study mathematical properties of an integro-differential equation that arises as a particular limit case in the study of individual cell-based model. We obtain global well-posedness for some classes of interaction potentials and finite time blow-up for others. The existence of space homogeneous steady states as well as long-time asymptotics for the solutions of the problem is also discussed.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2005.07.025