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A non-linear degenerate equation for direct aggregation and traveling wave dynamics.
Discrete Contin. Dyn. Syst.-Ser. B 13, 455-487 (2010)
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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Publication type
Article: Journal article
Document type
Scientific Article
Keywords
Direct aggregation; Degenerate diffusion; Traveling waves; Ill-posed problems; Negative diffusion
ISSN (print) / ISBN
1531-3492
e-ISSN
1553-524X
Quellenangaben
Volume: 13,
Issue: 2,
Pages: 455-487
Publisher
American Institute of Mathematical Sciences (AIMS)
Publishing Place
Springfield MO
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Biomathematics and Biometry (IBB)