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Sánchez-Garduno, F.* ; Maini, P.K.* ; Pérez-Velázquez, J.

A non-linear degenerate equation for direct aggregation and traveling wave dynamics.

Discrete Contin. Dyn. Syst.-Ser. B 13, 455-487 (2010)
DOI
The gregarious behavior of individuals of populations is an important factor in avoiding predators or for reproduction. Here, by using a random biased walk approach, we build a model which, after a transformation, takes the general form ut = [D(u)ux]x + g(u). The model involves a density-dependent non-linear diffusion coefficient D whose sign changes as the population density u increases. For negative values of D aggregation occurs, while dispersion occurs for positive values of D. We deal with a family of degenerate negative diffusion equations with logistic-like growth rate g. We study the one-dimensional traveling wave dynamics for these equations and illustrate our results with a couple of examples. A discussion of the ill-posedness of the partial differential equation problem is included.
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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Korrespondenzautor
Schlagwörter Direct aggregation; Degenerate diffusion; Traveling waves; Ill-posed problems; Negative diffusion
ISSN (print) / ISBN 1531-3492
e-ISSN 1553-524X
Zeitschrift Discrete and Continuous Dynamical Systems. Series B
Quellenangaben Band: 13, Heft: 2, Seiten: 455-487 Artikelnummer: , Supplement: ,
Verlag American Institute of Mathematical Sciences (AIMS)
Verlagsort Springfield MO
Nichtpatentliteratur Publikationen
Begutachtungsstatus Peer reviewed
Institut(e) Institute of Biomathematics and Biometry (IBB)