Bodnar, Marek and Velázquez, J.J. L. (2006) An integro-differential equation arising as a limit of individual cell-based models. Journal of Differential Equations, 222 (2). pp. 341-380. ISSN 0022-0396
Official URL: http://www.sciencedirect.com/science/journal/00220396
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.
|Uncontrolled Keywords:||Interacting Diffusion-Processes; Porous-medium Equation; Behavior; Law|
|Subjects:||Sciences > Mathematics > Differential equations|
|Deposited On:||28 Mar 2011 12:58|
|Last Modified:||30 Aug 2011 13:26|