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

Abstract:

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 [u_{t}=[D(u)u_{x}]_{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...

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Authors


F Sánchez-Garduño More by this author
P. K. Maini More by this author
J Pérez-Velázquez More by this author
Publication date:
2010
URN:
uuid:b7e6636f-e4bd-4490-82d9-4d61f0418691
Local pid:
oai:eprints.maths.ox.ac.uk:874

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