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- Title
The influence of a line with fast diffusion on Fisher-KPP propagation.
- Authors
Berestycki, Henri; Roquejoffre, Jean-Michel; Rossi, Luca
- Abstract
We propose here a new model to describe biological invasions in the plane when a strong diffusion takes place on a line. We establish the main properties of the system, and also derive the asymptotic speed of spreading in the direction of the line. For low diffusion, the line has no effect, whereas, past a threshold, the line enhances global diffusion in the plane and the propagation is directed by diffusion on the line. It is shown here that the global asymptotic speed of spreading in the plane, in the direction of the line, grows as the square root of the diffusion on the line. The model is much relevant to account for the effects of fast diffusion lines such as roads on spreading of invasive species.
- Subjects
BIOLOGICAL invasions; NATURAL selection; INTRODUCED species; ORGANISMS; NONINDIGENOUS pests; POPULATION biology
- Publication
Journal of Mathematical Biology, 2013, Vol 66, Issue 4/5, p743
- ISSN
0303-6812
- Publication type
Article
- DOI
10.1007/s00285-012-0604-z