Sánchez-Garduño , F and Maini, P. K. and Pérez-Velázquez, J (2010) A non-linear degenerate equation for direct aggregation and traveling wave dynamics. Discrete and Continuous Dynamical Systems Series B, 13 (2). pp. 455-487.
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_=[D(u)u_]_+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.
|Uncontrolled Keywords:||Direct aggregation, degenerate diffusion, traveling waves, ill-posed problems, negative diffusion.|
|Subjects:||A - C > Biology and other natural sciences|
|Research Groups:||Centre for Mathematical Biology|
|Deposited By:||Philip Maini|
|Deposited On:||19 Dec 2009 08:32|
|Last Modified:||25 Oct 2010 16:39|
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