SánchezGarduño, F and Maini, P. K. and PérezVelázquez, J (2010) A nonlinear degenerate equation for direct aggregation and traveling wave dynamics. Discrete and Continuous Dynamical Systems Series B, 13 (2). pp. 455487.

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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_=[D(u)u_]_+g(u)] . The model involves a densitydependent nonlinear 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 logisticlike growth rate [g] . We study the onedimensional traveling wave dynamics for these equations and illustrate our results with a couple of examples. A discussion of the illposedness of the partial differential equation problem is included.
Item Type:  Article 

Uncontrolled Keywords:  Direct aggregation, degenerate diffusion, traveling waves, illposed problems, negative diffusion. 
Subjects:  A  C > Biology and other natural sciences 
Research Groups:  Centre for Mathematical Biology 
ID Code:  874 
Deposited By:  Philip Maini 
Deposited On:  19 Dec 2009 08:32 
Last Modified:  29 May 2015 18:33 
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