ISSN:
1432-1416
Keywords:
Key words: Nonlinear advective processes
;
Traveling waves
;
Stability
Source:
Springer Online Journal Archives 1860-2000
Topics:
Biology
,
Mathematics
Notes:
Abstract. We establish the existence of traveling wave solutions for a nonlinear partial differential equation that models a logistically growing population whose movement is governed by an advective process. Conditions are presented for which traveling wave solutions exist and for which they are stable to small semi-finite domain perturbations. The wave is of mathematical interest because its behavior is determined by a singular differential equation and those with small speed of propagation steepen into a shock-like solutions. Finally, we indicate that the smoothing presence of diffusion allows wave persistence when an advective slow moving wave may collapse.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002850050152
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