Maini, P. K. and Malaguti, L. and Marcelli, C. and Matucci, S. (2006) Diffusion-aggregation processes with mono-stable reaction terms. Discrete and Continuous Dynamical Systems Series B, 6 (5). 1175 -1189.
This paper analyses front propagation of the equation
where is a monostable (ie Fisher-type) nonlinear reaction term and changes its sign once, from positive to negative values,in the interval where the process is studied. This model equation accounts for simultaneous diffusive and aggregative behaviors of a population dynamic depending on the population density at time and position . The existence of infinitely many travelling wave solutions is proven. These fronts are parametrized by their wave speed and monotonically connect the stationary states u = 0 and v = 1. In the degenerate case, i.e. when D(0) and/or D(1) = 0, sharp profiles appear, corresponding to the minimum wave speed. They also have new behaviors, in addition to those already observed in diffusive models, since they can be right compactly supported, left compactly supported, or both. The dynamics can exhibit, respectively, the phenomena of finite speed of propagation, finite speed of saturation, or both.
|Uncontrolled Keywords:||Diffusion-aggregation processes, population dynamics, front propagation, sharp profiles, finite speed of propagation.|
|Subjects:||A - C > Biology and other natural sciences|
|Research Groups:||Centre for Mathematical Biology|
|Deposited By:||Philip Maini|
|Deposited On:||08 Nov 2006|
|Last Modified:||20 Jul 2009 14:20|
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